[{"data":1,"prerenderedAt":3859},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintervalladditivitaet":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintervalladditivitaet":3849},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":101,"checks":3747,"conditions":3770,"conditionsHtml":3771,"deprecated":3772,"description":3741,"extension":3773,"figure":3774,"figureCaption":3775,"figureHtml":3817,"formulaId":3818,"latex":3819,"latexHtml":3820,"level":3821,"meta":3822,"navigation":3785,"path":3823,"redirectFrom":3824,"related":3825,"seo":3829,"stem":3830,"subject":577,"summary":3831,"tags":3832,"variables":3837,"__hash__":3848},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintervalladditivitaet.md","Intervalladditivität",[550,551,552,553,554],"Intervalladditivität Integral","Integral aufteilen","Integrationsgrenzen vertauschen","Integral zerlegen","Integral stückweise",{"type":556,"value":557,"toc":3740},"minimark",[558,563,675,678,1122,1298,1301,1316,1320,1524,2426,2620,2980,3012,3648,3652],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,613,614,643,644,674],"p",{},"Man kann den Integrationsweg von ",[568,569,572,594],"span",{"className":570},[571],"katex",[568,573,576],{"className":574},[575],"katex-mathml",[577,578,580],"math",{"xmlns":579},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[581,582,583,590],"semantics",{},[584,585,586],"mrow",{},[587,588,589],"mi",{},"a",[591,592,589],"annotation",{"encoding":593},"application\u002Fx-tex",[568,595,599],{"className":596,"ariaHidden":598},[597],"katex-html","true",[568,600,603,608],{"className":601},[602],"base",[568,604],{"className":605,"style":607},[606],"strut","height:0.4306em;",[568,609,589],{"className":610},[611,612],"mord","mathnormal"," nach ",[568,615,617,631],{"className":616},[571],[568,618,620],{"className":619},[575],[577,621,622],{"xmlns":579},[581,623,624,629],{},[584,625,626],{},[587,627,628],{},"c",[591,630,628],{"encoding":593},[568,632,634],{"className":633,"ariaHidden":598},[597],[568,635,637,640],{"className":636},[602],[568,638],{"className":639,"style":607},[606],[568,641,628],{"className":642},[611,612]," an einer beliebigen Stelle ",[568,645,647,661],{"className":646},[571],[568,648,650],{"className":649},[575],[577,651,652],{"xmlns":579},[581,653,654,659],{},[584,655,656],{},[587,657,658],{},"b",[591,660,658],{"encoding":593},[568,662,664],{"className":663,"ariaHidden":598},[597],[568,665,667,671],{"className":666},[602],[568,668],{"className":669,"style":670},[606],"height:0.6944em;",[568,672,658],{"className":673},[611,612]," unterbrechen. Die beiden Teilintegrale ergeben zusammen wieder das ganze Integral.",[564,676,677],{},"Dazu gehören zwei Festlegungen:",[679,680,681,873],"ul",{},[682,683,684,685,872],"li",{},"Gleiche Grenzen ergeben null: ",[568,686,688,740],{"className":687},[571],[568,689,691],{"className":690},[575],[577,692,693],{"xmlns":579},[581,694,695,737],{},[584,696,697,708,711,715,718,721,725,728,730,733],{},[698,699,700,704,706],"msubsup",{},[701,702,703],"mo",{},"∫",[587,705,589],{},[587,707,589],{},[587,709,710],{},"f",[701,712,714],{"stretchy":713},"false","(",[587,716,717],{},"x",[701,719,720],{"stretchy":713},")",[722,723,724],"mtext",{}," ",[587,726,727],{},"d",[587,729,717],{},[701,731,732],{},"=",[734,735,736],"mn",{},"0",[591,738,739],{"encoding":593},"\\int_a^a f(x)\\,dx = 0",[568,741,743,862],{"className":742,"ariaHidden":598},[597],[568,744,746,750,822,827,831,835,838,842,845,848,851,855,859],{"className":745},[602],[568,747],{"className":748,"style":749},[606],"height:1.2151em;vertical-align:-0.3558em;",[568,751,754,760],{"className":752},[753],"mop",[568,755,703],{"className":756,"style":759},[753,757,758],"op-symbol","small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[568,761,764],{"className":762},[763],"msupsub",[568,765,769,813],{"className":766},[767,768],"vlist-t","vlist-t2",[568,770,773,808],{"className":771},[772],"vlist-r",[568,774,778,796],{"className":775,"style":777},[776],"vlist","height:0.8593em;",[568,779,781,786],{"style":780},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[568,782],{"className":783,"style":785},[784],"pstrut","height:2.7em;",[568,787,793],{"className":788},[789,790,791,792],"sizing","reset-size6","size3","mtight",[568,794,589],{"className":795},[611,612,792],[568,797,799,802],{"style":798},"top:-3.2579em;margin-right:0.05em;",[568,800],{"className":801,"style":785},[784],[568,803,805],{"className":804},[789,790,791,792],[568,806,589],{"className":807},[611,612,792],[568,809,812],{"className":810},[811],"vlist-s","​",[568,814,816],{"className":815},[772],[568,817,820],{"className":818,"style":819},[776],"height:0.3558em;",[568,821],{},[568,823],{"className":824,"style":826},[825],"mspace","margin-right:0.1667em;",[568,828,710],{"className":829,"style":830},[611,612],"margin-right:0.1076em;",[568,832,714],{"className":833},[834],"mopen",[568,836,717],{"className":837},[611,612],[568,839,720],{"className":840},[841],"mclose",[568,843],{"className":844,"style":826},[825],[568,846,727],{"className":847},[611,612],[568,849,717],{"className":850},[611,612],[568,852],{"className":853,"style":854},[825],"margin-right:0.2778em;",[568,856,732],{"className":857},[858],"mrel",[568,860],{"className":861,"style":854},[825],[568,863,865,869],{"className":864},[602],[568,866],{"className":867,"style":868},[606],"height:0.6444em;",[568,870,736],{"className":871},[611],".",[682,874,875,876,872],{},"Vertauschte Grenzen ändern das Vorzeichen: ",[568,877,879,940],{"className":878},[571],[568,880,882],{"className":881},[575],[577,883,884],{"xmlns":579},[581,885,886,937],{},[584,887,888,896,898,900,902,904,906,908,910,912,915,923,925,927,929,931,933,935],{},[698,889,890,892,894],{},[701,891,703],{},[587,893,658],{},[587,895,589],{},[587,897,710],{},[701,899,714],{"stretchy":713},[587,901,717],{},[701,903,720],{"stretchy":713},[722,905,724],{},[587,907,727],{},[587,909,717],{},[701,911,732],{},[701,913,914],{},"−",[698,916,917,919,921],{},[701,918,703],{},[587,920,589],{},[587,922,658],{},[587,924,710],{},[701,926,714],{"stretchy":713},[587,928,717],{},[701,930,720],{"stretchy":713},[722,932,724],{},[587,934,727],{},[587,936,717],{},[591,938,939],{"encoding":593},"\\int_b^a f(x)\\,dx = -\\int_a^b f(x)\\,dx",[568,941,943,1033],{"className":942,"ariaHidden":598},[597],[568,944,946,949,1000,1003,1006,1009,1012,1015,1018,1021,1024,1027,1030],{"className":945},[602],[568,947],{"className":948,"style":749},[606],[568,950,952,955],{"className":951},[753],[568,953,703],{"className":954,"style":759},[753,757,758],[568,956,958],{"className":957},[763],[568,959,961,992],{"className":960},[767,768],[568,962,964,989],{"className":963},[772],[568,965,967,978],{"className":966,"style":777},[776],[568,968,969,972],{"style":780},[568,970],{"className":971,"style":785},[784],[568,973,975],{"className":974},[789,790,791,792],[568,976,658],{"className":977},[611,612,792],[568,979,980,983],{"style":798},[568,981],{"className":982,"style":785},[784],[568,984,986],{"className":985},[789,790,791,792],[568,987,589],{"className":988},[611,612,792],[568,990,812],{"className":991},[811],[568,993,995],{"className":994},[772],[568,996,998],{"className":997,"style":819},[776],[568,999],{},[568,1001],{"className":1002,"style":826},[825],[568,1004,710],{"className":1005,"style":830},[611,612],[568,1007,714],{"className":1008},[834],[568,1010,717],{"className":1011},[611,612],[568,1013,720],{"className":1014},[841],[568,1016],{"className":1017,"style":826},[825],[568,1019,727],{"className":1020},[611,612],[568,1022,717],{"className":1023},[611,612],[568,1025],{"className":1026,"style":854},[825],[568,1028,732],{"className":1029},[858],[568,1031],{"className":1032,"style":854},[825],[568,1034,1036,1040,1043,1046,1098,1101,1104,1107,1110,1113,1116,1119],{"className":1035},[602],[568,1037],{"className":1038,"style":1039},[606],"height:1.3998em;vertical-align:-0.3558em;",[568,1041,914],{"className":1042},[611],[568,1044],{"className":1045,"style":826},[825],[568,1047,1049,1052],{"className":1048},[753],[568,1050,703],{"className":1051,"style":759},[753,757,758],[568,1053,1055],{"className":1054},[763],[568,1056,1058,1090],{"className":1057},[767,768],[568,1059,1061,1087],{"className":1060},[772],[568,1062,1065,1076],{"className":1063,"style":1064},[776],"height:1.044em;",[568,1066,1067,1070],{"style":780},[568,1068],{"className":1069,"style":785},[784],[568,1071,1073],{"className":1072},[789,790,791,792],[568,1074,589],{"className":1075},[611,612,792],[568,1077,1078,1081],{"style":798},[568,1079],{"className":1080,"style":785},[784],[568,1082,1084],{"className":1083},[789,790,791,792],[568,1085,658],{"className":1086},[611,612,792],[568,1088,812],{"className":1089},[811],[568,1091,1093],{"className":1092},[772],[568,1094,1096],{"className":1095,"style":819},[776],[568,1097],{},[568,1099],{"className":1100,"style":826},[825],[568,1102,710],{"className":1103,"style":830},[611,612],[568,1105,714],{"className":1106},[834],[568,1108,717],{"className":1109},[611,612],[568,1111,720],{"className":1112},[841],[568,1114],{"className":1115,"style":826},[825],[568,1117,727],{"className":1118},[611,612],[568,1120,717],{"className":1121},[611,612],[564,1123,1124,1125,1153,1154,1182,1183,1211,1212,1240,1241,1182,1269,1297],{},"Mit diesen Festlegungen gilt die Regel für jede Lage von ",[568,1126,1128,1141],{"className":1127},[571],[568,1129,1131],{"className":1130},[575],[577,1132,1133],{"xmlns":579},[581,1134,1135,1139],{},[584,1136,1137],{},[587,1138,589],{},[591,1140,589],{"encoding":593},[568,1142,1144],{"className":1143,"ariaHidden":598},[597],[568,1145,1147,1150],{"className":1146},[602],[568,1148],{"className":1149,"style":607},[606],[568,1151,589],{"className":1152},[611,612],", ",[568,1155,1157,1170],{"className":1156},[571],[568,1158,1160],{"className":1159},[575],[577,1161,1162],{"xmlns":579},[581,1163,1164,1168],{},[584,1165,1166],{},[587,1167,658],{},[591,1169,658],{"encoding":593},[568,1171,1173],{"className":1172,"ariaHidden":598},[597],[568,1174,1176,1179],{"className":1175},[602],[568,1177],{"className":1178,"style":670},[606],[568,1180,658],{"className":1181},[611,612]," und ",[568,1184,1186,1199],{"className":1185},[571],[568,1187,1189],{"className":1188},[575],[577,1190,1191],{"xmlns":579},[581,1192,1193,1197],{},[584,1194,1195],{},[587,1196,628],{},[591,1198,628],{"encoding":593},[568,1200,1202],{"className":1201,"ariaHidden":598},[597],[568,1203,1205,1208],{"className":1204},[602],[568,1206],{"className":1207,"style":607},[606],[568,1209,628],{"className":1210},[611,612],", auch wenn ",[568,1213,1215,1228],{"className":1214},[571],[568,1216,1218],{"className":1217},[575],[577,1219,1220],{"xmlns":579},[581,1221,1222,1226],{},[584,1223,1224],{},[587,1225,658],{},[591,1227,658],{"encoding":593},[568,1229,1231],{"className":1230,"ariaHidden":598},[597],[568,1232,1234,1237],{"className":1233},[602],[568,1235],{"className":1236,"style":670},[606],[568,1238,658],{"className":1239},[611,612]," nicht zwischen ",[568,1242,1244,1257],{"className":1243},[571],[568,1245,1247],{"className":1246},[575],[577,1248,1249],{"xmlns":579},[581,1250,1251,1255],{},[584,1252,1253],{},[587,1254,589],{},[591,1256,589],{"encoding":593},[568,1258,1260],{"className":1259,"ariaHidden":598},[597],[568,1261,1263,1266],{"className":1262},[602],[568,1264],{"className":1265,"style":607},[606],[568,1267,589],{"className":1268},[611,612],[568,1270,1272,1285],{"className":1271},[571],[568,1273,1275],{"className":1274},[575],[577,1276,1277],{"xmlns":579},[581,1278,1279,1283],{},[584,1280,1281],{},[587,1282,628],{},[591,1284,628],{"encoding":593},[568,1286,1288],{"className":1287,"ariaHidden":598},[597],[568,1289,1291,1294],{"className":1290},[602],[568,1292],{"className":1293,"style":607},[606],[568,1295,628],{"className":1296},[611,612]," liegt.",[564,1299,1300],{},"Man braucht die Regel vor allem für zwei Aufgabentypen:",[679,1302,1303,1310],{},[682,1304,1305,1309],{},[1306,1307,1308],"strong",{},"Abschnittsweise definierte Funktionen"," und Beträge: Man teilt an den Stellen auf, an denen die Funktionsvorschrift wechselt.",[682,1311,1312,1315],{},[1306,1313,1314],{},"Flächenberechnung",": Man teilt an den Nullstellen auf und addiert die Beträge der Teilintegrale.",[559,1317,1319],{"id":1318},"beispiele","Beispiele",[564,1321,1322,1323,1376,1377,1412,1413,1376,1466,1494,1495,1523],{},"Die Betragsfunktion ist für ",[568,1324,1326,1345],{"className":1325},[571],[568,1327,1329],{"className":1328},[575],[577,1330,1331],{"xmlns":579},[581,1332,1333,1342],{},[584,1334,1335,1337,1340],{},[587,1336,717],{},[701,1338,1339],{},"\u003C",[734,1341,736],{},[591,1343,1344],{"encoding":593},"x \u003C 0",[568,1346,1348,1367],{"className":1347,"ariaHidden":598},[597],[568,1349,1351,1355,1358,1361,1364],{"className":1350},[602],[568,1352],{"className":1353,"style":1354},[606],"height:0.5782em;vertical-align:-0.0391em;",[568,1356,717],{"className":1357},[611,612],[568,1359],{"className":1360,"style":854},[825],[568,1362,1339],{"className":1363},[858],[568,1365],{"className":1366,"style":854},[825],[568,1368,1370,1373],{"className":1369},[602],[568,1371],{"className":1372,"style":868},[606],[568,1374,736],{"className":1375},[611]," gleich ",[568,1378,1380,1396],{"className":1379},[571],[568,1381,1383],{"className":1382},[575],[577,1384,1385],{"xmlns":579},[581,1386,1387,1393],{},[584,1388,1389,1391],{},[701,1390,914],{},[587,1392,717],{},[591,1394,1395],{"encoding":593},"-x",[568,1397,1399],{"className":1398,"ariaHidden":598},[597],[568,1400,1402,1406,1409],{"className":1401},[602],[568,1403],{"className":1404,"style":1405},[606],"height:0.6667em;vertical-align:-0.0833em;",[568,1407,914],{"className":1408},[611],[568,1410,717],{"className":1411},[611,612]," und für ",[568,1414,1416,1435],{"className":1415},[571],[568,1417,1419],{"className":1418},[575],[577,1420,1421],{"xmlns":579},[581,1422,1423,1432],{},[584,1424,1425,1427,1430],{},[587,1426,717],{},[701,1428,1429],{},"≥",[734,1431,736],{},[591,1433,1434],{"encoding":593},"x \\geq 0",[568,1436,1438,1457],{"className":1437,"ariaHidden":598},[597],[568,1439,1441,1445,1448,1451,1454],{"className":1440},[602],[568,1442],{"className":1443,"style":1444},[606],"height:0.7719em;vertical-align:-0.136em;",[568,1446,717],{"className":1447},[611,612],[568,1449],{"className":1450,"style":854},[825],[568,1452,1429],{"className":1453},[858],[568,1455],{"className":1456,"style":854},[825],[568,1458,1460,1463],{"className":1459},[602],[568,1461],{"className":1462,"style":868},[606],[568,1464,736],{"className":1465},[611],[568,1467,1469,1482],{"className":1468},[571],[568,1470,1472],{"className":1471},[575],[577,1473,1474],{"xmlns":579},[581,1475,1476,1480],{},[584,1477,1478],{},[587,1479,717],{},[591,1481,717],{"encoding":593},[568,1483,1485],{"className":1484,"ariaHidden":598},[597],[568,1486,1488,1491],{"className":1487},[602],[568,1489],{"className":1490,"style":607},[606],[568,1492,717],{"className":1493},[611,612],". Man teilt deshalb bei ",[568,1496,1498,1511],{"className":1497},[571],[568,1499,1501],{"className":1500},[575],[577,1502,1503],{"xmlns":579},[581,1504,1505,1509],{},[584,1506,1507],{},[734,1508,736],{},[591,1510,736],{"encoding":593},[568,1512,1514],{"className":1513,"ariaHidden":598},[597],[568,1515,1517,1520],{"className":1516},[602],[568,1518],{"className":1519,"style":868},[606],[568,1521,736],{"className":1522},[611]," auf:",[568,1525,1528],{"className":1526},[1527],"katex-display",[568,1529,1531,1691],{"className":1530},[571],[568,1532,1534],{"className":1533},[575],[577,1535,1537],{"xmlns":579,"display":1536},"block",[581,1538,1539,1688],{},[584,1540,1541,1555,1559,1561,1563,1565,1567,1569,1571,1583,1585,1587,1589,1591,1593,1595,1597,1600,1608,1610,1612,1614,1616,1618,1650,1652,1674,1676,1678,1680,1683,1685],{},[698,1542,1543,1545,1552],{},[701,1544,703],{},[584,1546,1547,1549],{},[701,1548,914],{},[734,1550,1551],{},"2",[734,1553,1554],{},"3",[587,1556,1558],{"mathvariant":1557},"normal","∣",[587,1560,717],{},[587,1562,1558],{"mathvariant":1557},[722,1564,724],{},[587,1566,727],{},[587,1568,717],{},[701,1570,732],{},[698,1572,1573,1575,1581],{},[701,1574,703],{},[584,1576,1577,1579],{},[701,1578,914],{},[734,1580,1551],{},[734,1582,736],{},[701,1584,714],{"stretchy":713},[701,1586,914],{},[587,1588,717],{},[701,1590,720],{"stretchy":713},[722,1592,724],{},[587,1594,727],{},[587,1596,717],{},[701,1598,1599],{},"+",[698,1601,1602,1604,1606],{},[701,1603,703],{},[734,1605,736],{},[734,1607,1554],{},[587,1609,717],{},[722,1611,724],{},[587,1613,727],{},[587,1615,717],{},[701,1617,732],{},[698,1619,1620,1642,1648],{},[584,1621,1622,1625,1627,1639],{},[701,1623,1624],{"fence":598},"[",[701,1626,914],{},[1628,1629,1630,1637],"mfrac",{},[1631,1632,1633,1635],"msup",{},[587,1634,717],{},[734,1636,1551],{},[734,1638,1551],{},[701,1640,1641],{"fence":598},"]",[584,1643,1644,1646],{},[701,1645,914],{},[734,1647,1551],{},[734,1649,736],{},[701,1651,1599],{},[698,1653,1654,1670,1672],{},[584,1655,1656,1658,1668],{},[701,1657,1624],{"fence":598},[1628,1659,1660,1666],{},[1631,1661,1662,1664],{},[587,1663,717],{},[734,1665,1551],{},[734,1667,1551],{},[701,1669,1641],{"fence":598},[734,1671,736],{},[734,1673,1554],{},[701,1675,732],{},[734,1677,1551],{},[701,1679,1599],{},[734,1681,1682],{},"4,5",[701,1684,732],{},[734,1686,1687],{},"6,5",[591,1689,1690],{"encoding":593},"\\int_{-2}^{3} |x|\\,dx = \\int_{-2}^{0} (-x)\\,dx + \\int_{0}^{3} x\\,dx = \\left[-\\frac{x^2}{2}\\right]_{-2}^{0} + \\left[\\frac{x^2}{2}\\right]_{0}^{3} = 2 + 4{,}5 = 6{,}5",[568,1692,1694,1797,1895,1984,2182,2356,2375,2407],{"className":1693,"ariaHidden":598},[597],[568,1695,1697,1701,1767,1770,1773,1776,1779,1782,1785,1788,1791,1794],{"className":1696},[602],[568,1698],{"className":1699,"style":1700},[606],"height:2.5343em;vertical-align:-0.9703em;",[568,1702,1704,1709],{"className":1703},[753],[568,1705,703],{"className":1706,"style":1708},[753,757,1707],"large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[568,1710,1712],{"className":1711},[763],[568,1713,1715,1758],{"className":1714},[767,768],[568,1716,1718,1755],{"className":1717},[772],[568,1719,1722,1740],{"className":1720,"style":1721},[776],"height:1.564em;",[568,1723,1725,1728],{"style":1724},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[568,1726],{"className":1727,"style":785},[784],[568,1729,1731],{"className":1730},[789,790,791,792],[568,1732,1734,1737],{"className":1733},[611,792],[568,1735,914],{"className":1736},[611,792],[568,1738,1551],{"className":1739},[611,792],[568,1741,1743,1746],{"style":1742},"top:-3.8129em;margin-right:0.05em;",[568,1744],{"className":1745,"style":785},[784],[568,1747,1749],{"className":1748},[789,790,791,792],[568,1750,1752],{"className":1751},[611,792],[568,1753,1554],{"className":1754},[611,792],[568,1756,812],{"className":1757},[811],[568,1759,1761],{"className":1760},[772],[568,1762,1765],{"className":1763,"style":1764},[776],"height:0.9703em;",[568,1766],{},[568,1768],{"className":1769,"style":826},[825],[568,1771,1558],{"className":1772},[611],[568,1774,717],{"className":1775},[611,612],[568,1777,1558],{"className":1778},[611],[568,1780],{"className":1781,"style":826},[825],[568,1783,727],{"className":1784},[611,612],[568,1786,717],{"className":1787},[611,612],[568,1789],{"className":1790,"style":854},[825],[568,1792,732],{"className":1793},[858],[568,1795],{"className":1796,"style":854},[825],[568,1798,1800,1803,1863,1866,1869,1872,1875,1878,1881,1884,1888,1892],{"className":1799},[602],[568,1801],{"className":1802,"style":1700},[606],[568,1804,1806,1809],{"className":1805},[753],[568,1807,703],{"className":1808,"style":1708},[753,757,1707],[568,1810,1812],{"className":1811},[763],[568,1813,1815,1855],{"className":1814},[767,768],[568,1816,1818,1852],{"className":1817},[772],[568,1819,1821,1838],{"className":1820,"style":1721},[776],[568,1822,1823,1826],{"style":1724},[568,1824],{"className":1825,"style":785},[784],[568,1827,1829],{"className":1828},[789,790,791,792],[568,1830,1832,1835],{"className":1831},[611,792],[568,1833,914],{"className":1834},[611,792],[568,1836,1551],{"className":1837},[611,792],[568,1839,1840,1843],{"style":1742},[568,1841],{"className":1842,"style":785},[784],[568,1844,1846],{"className":1845},[789,790,791,792],[568,1847,1849],{"className":1848},[611,792],[568,1850,736],{"className":1851},[611,792],[568,1853,812],{"className":1854},[811],[568,1856,1858],{"className":1857},[772],[568,1859,1861],{"className":1860,"style":1764},[776],[568,1862],{},[568,1864,714],{"className":1865},[834],[568,1867,914],{"className":1868},[611],[568,1870,717],{"className":1871},[611,612],[568,1873,720],{"className":1874},[841],[568,1876],{"className":1877,"style":826},[825],[568,1879,727],{"className":1880},[611,612],[568,1882,717],{"className":1883},[611,612],[568,1885],{"className":1886,"style":1887},[825],"margin-right:0.2222em;",[568,1889,1599],{"className":1890},[1891],"mbin",[568,1893],{"className":1894,"style":1887},[825],[568,1896,1898,1902,1960,1963,1966,1969,1972,1975,1978,1981],{"className":1897},[602],[568,1899],{"className":1900,"style":1901},[606],"height:2.476em;vertical-align:-0.9119em;",[568,1903,1905,1908],{"className":1904},[753],[568,1906,703],{"className":1907,"style":1708},[753,757,1707],[568,1909,1911],{"className":1910},[763],[568,1912,1914,1951],{"className":1913},[767,768],[568,1915,1917,1948],{"className":1916},[772],[568,1918,1920,1934],{"className":1919,"style":1721},[776],[568,1921,1922,1925],{"style":1724},[568,1923],{"className":1924,"style":785},[784],[568,1926,1928],{"className":1927},[789,790,791,792],[568,1929,1931],{"className":1930},[611,792],[568,1932,736],{"className":1933},[611,792],[568,1935,1936,1939],{"style":1742},[568,1937],{"className":1938,"style":785},[784],[568,1940,1942],{"className":1941},[789,790,791,792],[568,1943,1945],{"className":1944},[611,792],[568,1946,1554],{"className":1947},[611,792],[568,1949,812],{"className":1950},[811],[568,1952,1954],{"className":1953},[772],[568,1955,1958],{"className":1956,"style":1957},[776],"height:0.9119em;",[568,1959],{},[568,1961],{"className":1962,"style":826},[825],[568,1964,717],{"className":1965},[611,612],[568,1967],{"className":1968,"style":826},[825],[568,1970,727],{"className":1971},[611,612],[568,1973,717],{"className":1974},[611,612],[568,1976],{"className":1977,"style":854},[825],[568,1979,732],{"className":1980},[858],[568,1982],{"className":1983,"style":854},[825],[568,1985,1987,1991,2173,2176,2179],{"className":1986},[602],[568,1988],{"className":1989,"style":1990},[606],"height:2.7532em;vertical-align:-1.0581em;",[568,1992,1995,2115],{"className":1993},[1994],"minner",[568,1996,1998,2007,2010,2109],{"className":1997},[1994],[568,1999,2003],{"className":2000,"style":2002},[834,2001],"delimcenter","top:0em;",[568,2004,1624],{"className":2005},[2006,791],"delimsizing",[568,2008,914],{"className":2009},[611],[568,2011,2013,2017,2106],{"className":2012},[611],[568,2014],{"className":2015},[834,2016],"nulldelimiter",[568,2018,2020],{"className":2019},[1628],[568,2021,2023,2097],{"className":2022},[767,768],[568,2024,2026,2094],{"className":2025},[772],[568,2027,2030,2043,2054],{"className":2028,"style":2029},[776],"height:1.4911em;",[568,2031,2033,2037],{"style":2032},"top:-2.314em;",[568,2034],{"className":2035,"style":2036},[784],"height:3em;",[568,2038,2040],{"className":2039},[611],[568,2041,1551],{"className":2042},[611],[568,2044,2046,2049],{"style":2045},"top:-3.23em;",[568,2047],{"className":2048,"style":2036},[784],[568,2050],{"className":2051,"style":2053},[2052],"frac-line","border-bottom-width:0.04em;",[568,2055,2057,2060],{"style":2056},"top:-3.677em;",[568,2058],{"className":2059,"style":2036},[784],[568,2061,2063],{"className":2062},[611],[568,2064,2066,2069],{"className":2065},[611],[568,2067,717],{"className":2068},[611,612],[568,2070,2072],{"className":2071},[763],[568,2073,2075],{"className":2074},[767],[568,2076,2078],{"className":2077},[772],[568,2079,2082],{"className":2080,"style":2081},[776],"height:0.8141em;",[568,2083,2085,2088],{"style":2084},"top:-3.063em;margin-right:0.05em;",[568,2086],{"className":2087,"style":785},[784],[568,2089,2091],{"className":2090},[789,790,791,792],[568,2092,1551],{"className":2093},[611,792],[568,2095,812],{"className":2096},[811],[568,2098,2100],{"className":2099},[772],[568,2101,2104],{"className":2102,"style":2103},[776],"height:0.686em;",[568,2105],{},[568,2107],{"className":2108},[841,2016],[568,2110,2112],{"className":2111,"style":2002},[841,2001],[568,2113,1641],{"className":2114},[2006,791],[568,2116,2118],{"className":2117},[763],[568,2119,2121,2164],{"className":2120},[767,768],[568,2122,2124,2161],{"className":2123},[772],[568,2125,2128,2146],{"className":2126,"style":2127},[776],"height:1.6951em;",[568,2129,2131,2134],{"style":2130},"top:-1.7003em;margin-right:0.05em;",[568,2132],{"className":2133,"style":785},[784],[568,2135,2137],{"className":2136},[789,790,791,792],[568,2138,2140,2143],{"className":2139},[611,792],[568,2141,914],{"className":2142},[611,792],[568,2144,1551],{"className":2145},[611,792],[568,2147,2149,2152],{"style":2148},"top:-3.944em;margin-right:0.05em;",[568,2150],{"className":2151,"style":785},[784],[568,2153,2155],{"className":2154},[789,790,791,792],[568,2156,2158],{"className":2157},[611,792],[568,2159,736],{"className":2160},[611,792],[568,2162,812],{"className":2163},[811],[568,2165,2167],{"className":2166},[772],[568,2168,2171],{"className":2169,"style":2170},[776],"height:1.0581em;",[568,2172],{},[568,2174],{"className":2175,"style":1887},[825],[568,2177,1599],{"className":2178},[1891],[568,2180],{"className":2181,"style":1887},[825],[568,2183,2185,2189,2347,2350,2353],{"className":2184},[602],[568,2186],{"className":2187,"style":2188},[606],"height:2.6948em;vertical-align:-0.9997em;",[568,2190,2192,2295],{"className":2191},[1994],[568,2193,2195,2201,2289],{"className":2194},[1994],[568,2196,2198],{"className":2197,"style":2002},[834,2001],[568,2199,1624],{"className":2200},[2006,791],[568,2202,2204,2207,2286],{"className":2203},[611],[568,2205],{"className":2206},[834,2016],[568,2208,2210],{"className":2209},[1628],[568,2211,2213,2278],{"className":2212},[767,768],[568,2214,2216,2275],{"className":2215},[772],[568,2217,2219,2230,2238],{"className":2218,"style":2029},[776],[568,2220,2221,2224],{"style":2032},[568,2222],{"className":2223,"style":2036},[784],[568,2225,2227],{"className":2226},[611],[568,2228,1551],{"className":2229},[611],[568,2231,2232,2235],{"style":2045},[568,2233],{"className":2234,"style":2036},[784],[568,2236],{"className":2237,"style":2053},[2052],[568,2239,2240,2243],{"style":2056},[568,2241],{"className":2242,"style":2036},[784],[568,2244,2246],{"className":2245},[611],[568,2247,2249,2252],{"className":2248},[611],[568,2250,717],{"className":2251},[611,612],[568,2253,2255],{"className":2254},[763],[568,2256,2258],{"className":2257},[767],[568,2259,2261],{"className":2260},[772],[568,2262,2264],{"className":2263,"style":2081},[776],[568,2265,2266,2269],{"style":2084},[568,2267],{"className":2268,"style":785},[784],[568,2270,2272],{"className":2271},[789,790,791,792],[568,2273,1551],{"className":2274},[611,792],[568,2276,812],{"className":2277},[811],[568,2279,2281],{"className":2280},[772],[568,2282,2284],{"className":2283,"style":2103},[776],[568,2285],{},[568,2287],{"className":2288},[841,2016],[568,2290,2292],{"className":2291,"style":2002},[841,2001],[568,2293,1641],{"className":2294},[2006,791],[568,2296,2298],{"className":2297},[763],[568,2299,2301,2338],{"className":2300},[767,768],[568,2302,2304,2335],{"className":2303},[772],[568,2305,2307,2321],{"className":2306,"style":2127},[776],[568,2308,2309,2312],{"style":2130},[568,2310],{"className":2311,"style":785},[784],[568,2313,2315],{"className":2314},[789,790,791,792],[568,2316,2318],{"className":2317},[611,792],[568,2319,736],{"className":2320},[611,792],[568,2322,2323,2326],{"style":2148},[568,2324],{"className":2325,"style":785},[784],[568,2327,2329],{"className":2328},[789,790,791,792],[568,2330,2332],{"className":2331},[611,792],[568,2333,1554],{"className":2334},[611,792],[568,2336,812],{"className":2337},[811],[568,2339,2341],{"className":2340},[772],[568,2342,2345],{"className":2343,"style":2344},[776],"height:0.9997em;",[568,2346],{},[568,2348],{"className":2349,"style":854},[825],[568,2351,732],{"className":2352},[858],[568,2354],{"className":2355,"style":854},[825],[568,2357,2359,2363,2366,2369,2372],{"className":2358},[602],[568,2360],{"className":2361,"style":2362},[606],"height:0.7278em;vertical-align:-0.0833em;",[568,2364,1551],{"className":2365},[611],[568,2367],{"className":2368,"style":1887},[825],[568,2370,1599],{"className":2371},[1891],[568,2373],{"className":2374,"style":1887},[825],[568,2376,2378,2382,2386,2394,2398,2401,2404],{"className":2377},[602],[568,2379],{"className":2380,"style":2381},[606],"height:0.8389em;vertical-align:-0.1944em;",[568,2383,2385],{"className":2384},[611],"4",[568,2387,2389],{"className":2388},[611],[568,2390,2393],{"className":2391},[2392],"mpunct",",",[568,2395,2397],{"className":2396},[611],"5",[568,2399],{"className":2400,"style":854},[825],[568,2402,732],{"className":2403},[858],[568,2405],{"className":2406,"style":854},[825],[568,2408,2410,2413,2417,2423],{"className":2409},[602],[568,2411],{"className":2412,"style":2381},[606],[568,2414,2416],{"className":2415},[611],"6",[568,2418,2420],{"className":2419},[611],[568,2421,2393],{"className":2422},[2392],[568,2424,2397],{"className":2425},[611],[564,2427,2428,2429,2526,2527,1182,2562,2590,2591,2619],{},"Die Funktion ",[568,2430,2432,2460],{"className":2431},[571],[568,2433,2435],{"className":2434},[575],[577,2436,2437],{"xmlns":579},[581,2438,2439,2457],{},[584,2440,2441,2443,2445,2447,2449,2451],{},[587,2442,710],{},[701,2444,714],{"stretchy":713},[587,2446,717],{},[701,2448,720],{"stretchy":713},[701,2450,732],{},[1631,2452,2453,2455],{},[587,2454,717],{},[734,2456,1554],{},[591,2458,2459],{"encoding":593},"f(x) = x^3",[568,2461,2463,2491],{"className":2462,"ariaHidden":598},[597],[568,2464,2466,2470,2473,2476,2479,2482,2485,2488],{"className":2465},[602],[568,2467],{"className":2468,"style":2469},[606],"height:1em;vertical-align:-0.25em;",[568,2471,710],{"className":2472,"style":830},[611,612],[568,2474,714],{"className":2475},[834],[568,2477,717],{"className":2478},[611,612],[568,2480,720],{"className":2481},[841],[568,2483],{"className":2484,"style":854},[825],[568,2486,732],{"className":2487},[858],[568,2489],{"className":2490,"style":854},[825],[568,2492,2494,2497],{"className":2493},[602],[568,2495],{"className":2496,"style":2081},[606],[568,2498,2500,2503],{"className":2499},[611],[568,2501,717],{"className":2502},[611,612],[568,2504,2506],{"className":2505},[763],[568,2507,2509],{"className":2508},[767],[568,2510,2512],{"className":2511},[772],[568,2513,2515],{"className":2514,"style":2081},[776],[568,2516,2517,2520],{"style":2084},[568,2518],{"className":2519,"style":785},[784],[568,2521,2523],{"className":2522},[789,790,791,792],[568,2524,1554],{"className":2525},[611,792]," hat zwischen ",[568,2528,2530,2547],{"className":2529},[571],[568,2531,2533],{"className":2532},[575],[577,2534,2535],{"xmlns":579},[581,2536,2537,2544],{},[584,2538,2539,2541],{},[701,2540,914],{},[734,2542,2543],{},"1",[591,2545,2546],{"encoding":593},"-1",[568,2548,2550],{"className":2549,"ariaHidden":598},[597],[568,2551,2553,2556,2559],{"className":2552},[602],[568,2554],{"className":2555,"style":2362},[606],[568,2557,914],{"className":2558},[611],[568,2560,2543],{"className":2561},[611],[568,2563,2565,2578],{"className":2564},[571],[568,2566,2568],{"className":2567},[575],[577,2569,2570],{"xmlns":579},[581,2571,2572,2576],{},[584,2573,2574],{},[734,2575,1551],{},[591,2577,1551],{"encoding":593},[568,2579,2581],{"className":2580,"ariaHidden":598},[597],[568,2582,2584,2587],{"className":2583},[602],[568,2585],{"className":2586,"style":868},[606],[568,2588,1551],{"className":2589},[611]," die Nullstelle ",[568,2592,2594,2607],{"className":2593},[571],[568,2595,2597],{"className":2596},[575],[577,2598,2599],{"xmlns":579},[581,2600,2601,2605],{},[584,2602,2603],{},[734,2604,736],{},[591,2606,736],{"encoding":593},[568,2608,2610],{"className":2609,"ariaHidden":598},[597],[568,2611,2613,2616],{"className":2612},[602],[568,2614],{"className":2615,"style":868},[606],[568,2617,736],{"className":2618},[611],". Das Integral liefert nur die Flächenbilanz:",[568,2621,2623],{"className":2622},[1527],[568,2624,2626,2684],{"className":2625},[571],[568,2627,2629],{"className":2628},[575],[577,2630,2631],{"xmlns":579,"display":1536},[581,2632,2633,2681],{},[584,2634,2635,2647,2653,2655,2657,2659,2661,2668,2670,2676,2678],{},[698,2636,2637,2639,2645],{},[701,2638,703],{},[584,2640,2641,2643],{},[701,2642,914],{},[734,2644,2543],{},[734,2646,1551],{},[1631,2648,2649,2651],{},[587,2650,717],{},[734,2652,1554],{},[722,2654,724],{},[587,2656,727],{},[587,2658,717],{},[701,2660,732],{},[1628,2662,2663,2666],{},[734,2664,2665],{},"16",[734,2667,2385],{},[701,2669,914],{},[1628,2671,2672,2674],{},[734,2673,2543],{},[734,2675,2385],{},[701,2677,732],{},[734,2679,2680],{},"3,75",[591,2682,2683],{"encoding":593},"\\int_{-1}^{2} x^3\\,dx = \\frac{16}{4} - \\frac{1}{4} = 3{,}75",[568,2685,2687,2805,2884,2961],{"className":2686,"ariaHidden":598},[597],[568,2688,2690,2693,2753,2756,2787,2790,2793,2796,2799,2802],{"className":2689},[602],[568,2691],{"className":2692,"style":1700},[606],[568,2694,2696,2699],{"className":2695},[753],[568,2697,703],{"className":2698,"style":1708},[753,757,1707],[568,2700,2702],{"className":2701},[763],[568,2703,2705,2745],{"className":2704},[767,768],[568,2706,2708,2742],{"className":2707},[772],[568,2709,2711,2728],{"className":2710,"style":1721},[776],[568,2712,2713,2716],{"style":1724},[568,2714],{"className":2715,"style":785},[784],[568,2717,2719],{"className":2718},[789,790,791,792],[568,2720,2722,2725],{"className":2721},[611,792],[568,2723,914],{"className":2724},[611,792],[568,2726,2543],{"className":2727},[611,792],[568,2729,2730,2733],{"style":1742},[568,2731],{"className":2732,"style":785},[784],[568,2734,2736],{"className":2735},[789,790,791,792],[568,2737,2739],{"className":2738},[611,792],[568,2740,1551],{"className":2741},[611,792],[568,2743,812],{"className":2744},[811],[568,2746,2748],{"className":2747},[772],[568,2749,2751],{"className":2750,"style":1764},[776],[568,2752],{},[568,2754],{"className":2755,"style":826},[825],[568,2757,2759,2762],{"className":2758},[611],[568,2760,717],{"className":2761},[611,612],[568,2763,2765],{"className":2764},[763],[568,2766,2768],{"className":2767},[767],[568,2769,2771],{"className":2770},[772],[568,2772,2775],{"className":2773,"style":2774},[776],"height:0.8641em;",[568,2776,2778,2781],{"style":2777},"top:-3.113em;margin-right:0.05em;",[568,2779],{"className":2780,"style":785},[784],[568,2782,2784],{"className":2783},[789,790,791,792],[568,2785,1554],{"className":2786},[611,792],[568,2788],{"className":2789,"style":826},[825],[568,2791,727],{"className":2792},[611,612],[568,2794,717],{"className":2795},[611,612],[568,2797],{"className":2798,"style":854},[825],[568,2800,732],{"className":2801},[858],[568,2803],{"className":2804,"style":854},[825],[568,2806,2808,2812,2875,2878,2881],{"className":2807},[602],[568,2809],{"className":2810,"style":2811},[606],"height:2.0074em;vertical-align:-0.686em;",[568,2813,2815,2818,2872],{"className":2814},[611],[568,2816],{"className":2817},[834,2016],[568,2819,2821],{"className":2820},[1628],[568,2822,2824,2864],{"className":2823},[767,768],[568,2825,2827,2861],{"className":2826},[772],[568,2828,2831,2842,2850],{"className":2829,"style":2830},[776],"height:1.3214em;",[568,2832,2833,2836],{"style":2032},[568,2834],{"className":2835,"style":2036},[784],[568,2837,2839],{"className":2838},[611],[568,2840,2385],{"className":2841},[611],[568,2843,2844,2847],{"style":2045},[568,2845],{"className":2846,"style":2036},[784],[568,2848],{"className":2849,"style":2053},[2052],[568,2851,2852,2855],{"style":2056},[568,2853],{"className":2854,"style":2036},[784],[568,2856,2858],{"className":2857},[611],[568,2859,2665],{"className":2860},[611],[568,2862,812],{"className":2863},[811],[568,2865,2867],{"className":2866},[772],[568,2868,2870],{"className":2869,"style":2103},[776],[568,2871],{},[568,2873],{"className":2874},[841,2016],[568,2876],{"className":2877,"style":1887},[825],[568,2879,914],{"className":2880},[1891],[568,2882],{"className":2883,"style":1887},[825],[568,2885,2887,2890,2952,2955,2958],{"className":2886},[602],[568,2888],{"className":2889,"style":2811},[606],[568,2891,2893,2896,2949],{"className":2892},[611],[568,2894],{"className":2895},[834,2016],[568,2897,2899],{"className":2898},[1628],[568,2900,2902,2941],{"className":2901},[767,768],[568,2903,2905,2938],{"className":2904},[772],[568,2906,2908,2919,2927],{"className":2907,"style":2830},[776],[568,2909,2910,2913],{"style":2032},[568,2911],{"className":2912,"style":2036},[784],[568,2914,2916],{"className":2915},[611],[568,2917,2385],{"className":2918},[611],[568,2920,2921,2924],{"style":2045},[568,2922],{"className":2923,"style":2036},[784],[568,2925],{"className":2926,"style":2053},[2052],[568,2928,2929,2932],{"style":2056},[568,2930],{"className":2931,"style":2036},[784],[568,2933,2935],{"className":2934},[611],[568,2936,2543],{"className":2937},[611],[568,2939,812],{"className":2940},[811],[568,2942,2944],{"className":2943},[772],[568,2945,2947],{"className":2946,"style":2103},[776],[568,2948],{},[568,2950],{"className":2951},[841,2016],[568,2953],{"className":2954,"style":854},[825],[568,2956,732],{"className":2957},[858],[568,2959],{"className":2960,"style":854},[825],[568,2962,2964,2967,2970,2976],{"className":2963},[602],[568,2965],{"className":2966,"style":2381},[606],[568,2968,1554],{"className":2969},[611],[568,2971,2973],{"className":2972},[611],[568,2974,2393],{"className":2975},[2392],[568,2977,2979],{"className":2978},[611],"75",[564,2981,2982,2983,3011],{},"Für die Fläche teilt man bei ",[568,2984,2986,2999],{"className":2985},[571],[568,2987,2989],{"className":2988},[575],[577,2990,2991],{"xmlns":579},[581,2992,2993,2997],{},[584,2994,2995],{},[734,2996,736],{},[591,2998,736],{"encoding":593},[568,3000,3002],{"className":3001,"ariaHidden":598},[597],[568,3003,3005,3008],{"className":3004},[602],[568,3006],{"className":3007,"style":868},[606],[568,3009,736],{"className":3010},[611]," auf und nimmt die Beträge:",[568,3013,3015],{"className":3014},[1527],[568,3016,3018,3112],{"className":3017},[571],[568,3019,3021],{"className":3020},[575],[577,3022,3023],{"xmlns":579,"display":1536},[581,3024,3025,3109],{},[584,3026,3027,3030,3032,3062,3064,3072,3078,3080,3082,3084,3086,3100,3102,3104,3106],{},[587,3028,3029],{},"A",[701,3031,732],{},[584,3033,3034,3036,3048,3054,3056,3058,3060],{},[701,3035,1558],{"fence":598},[698,3037,3038,3040,3046],{},[701,3039,703],{},[584,3041,3042,3044],{},[701,3043,914],{},[734,3045,2543],{},[734,3047,736],{},[1631,3049,3050,3052],{},[587,3051,717],{},[734,3053,1554],{},[722,3055,724],{},[587,3057,727],{},[587,3059,717],{},[701,3061,1558],{"fence":598},[701,3063,1599],{},[698,3065,3066,3068,3070],{},[701,3067,703],{},[734,3069,736],{},[734,3071,1551],{},[1631,3073,3074,3076],{},[587,3075,717],{},[734,3077,1554],{},[722,3079,724],{},[587,3081,727],{},[587,3083,717],{},[701,3085,732],{},[584,3087,3088,3090,3092,3098],{},[701,3089,1558],{"fence":598},[701,3091,914],{},[1628,3093,3094,3096],{},[734,3095,2543],{},[734,3097,2385],{},[701,3099,1558],{"fence":598},[701,3101,1599],{},[734,3103,2385],{},[701,3105,732],{},[734,3107,3108],{},"4,25",[591,3110,3111],{"encoding":593},"A = \\left|\\int_{-1}^{0} x^3\\,dx\\right| + \\int_{0}^{2} x^3\\,dx = \\left|-\\frac{1}{4}\\right| + 4 = 4{,}25",[568,3113,3115,3134,3340,3453,3611,3629],{"className":3114,"ariaHidden":598},[597],[568,3116,3118,3122,3125,3128,3131],{"className":3117},[602],[568,3119],{"className":3120,"style":3121},[606],"height:0.6833em;",[568,3123,3029],{"className":3124},[611,612],[568,3126],{"className":3127,"style":854},[825],[568,3129,732],{"className":3130},[858],[568,3132],{"className":3133,"style":854},[825],[568,3135,3137,3140,3331,3334,3337],{"className":3136},[602],[568,3138],{"className":3139,"style":1700},[606],[568,3141,3143,3193,3253,3256,3285,3288,3291,3294],{"className":3142},[1994],[568,3144,3146],{"className":3145},[834],[568,3147,3150],{"className":3148},[2006,3149],"mult",[568,3151,3153,3184],{"className":3152},[767,768],[568,3154,3156,3181],{"className":3155},[772],[568,3157,3160],{"className":3158,"style":3159},[776],"height:1.45em;",[568,3161,3163,3167],{"style":3162},"top:-3.45em;",[568,3164],{"className":3165,"style":3166},[784],"height:4.4em;",[568,3168,3170],{"style":3169},"width:0.333em;height:2.4em;",[3171,3172,3177],"svg",{"xmlns":3173,"width":3174,"height":3175,"viewBox":3176},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.333em","2.4em","0 0 333 2400",[3178,3179],"path",{"d":3180},"M145 15 v585 v1200 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-1200 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v1200 v585 h43z",[568,3182,812],{"className":3183},[811],[568,3185,3187],{"className":3186},[772],[568,3188,3191],{"className":3189,"style":3190},[776],"height:0.95em;",[568,3192],{},[568,3194,3196,3199],{"className":3195},[753],[568,3197,703],{"className":3198,"style":1708},[753,757,1707],[568,3200,3202],{"className":3201},[763],[568,3203,3205,3245],{"className":3204},[767,768],[568,3206,3208,3242],{"className":3207},[772],[568,3209,3211,3228],{"className":3210,"style":1721},[776],[568,3212,3213,3216],{"style":1724},[568,3214],{"className":3215,"style":785},[784],[568,3217,3219],{"className":3218},[789,790,791,792],[568,3220,3222,3225],{"className":3221},[611,792],[568,3223,914],{"className":3224},[611,792],[568,3226,2543],{"className":3227},[611,792],[568,3229,3230,3233],{"style":1742},[568,3231],{"className":3232,"style":785},[784],[568,3234,3236],{"className":3235},[789,790,791,792],[568,3237,3239],{"className":3238},[611,792],[568,3240,736],{"className":3241},[611,792],[568,3243,812],{"className":3244},[811],[568,3246,3248],{"className":3247},[772],[568,3249,3251],{"className":3250,"style":1764},[776],[568,3252],{},[568,3254],{"className":3255,"style":826},[825],[568,3257,3259,3262],{"className":3258},[611],[568,3260,717],{"className":3261},[611,612],[568,3263,3265],{"className":3264},[763],[568,3266,3268],{"className":3267},[767],[568,3269,3271],{"className":3270},[772],[568,3272,3274],{"className":3273,"style":2774},[776],[568,3275,3276,3279],{"style":2777},[568,3277],{"className":3278,"style":785},[784],[568,3280,3282],{"className":3281},[789,790,791,792],[568,3283,1554],{"className":3284},[611,792],[568,3286],{"className":3287,"style":826},[825],[568,3289,727],{"className":3290},[611,612],[568,3292,717],{"className":3293},[611,612],[568,3295,3297],{"className":3296},[841],[568,3298,3300],{"className":3299},[2006,3149],[568,3301,3303,3323],{"className":3302},[767,768],[568,3304,3306,3320],{"className":3305},[772],[568,3307,3309],{"className":3308,"style":3159},[776],[568,3310,3311,3314],{"style":3162},[568,3312],{"className":3313,"style":3166},[784],[568,3315,3316],{"style":3169},[3171,3317,3318],{"xmlns":3173,"width":3174,"height":3175,"viewBox":3176},[3178,3319],{"d":3180},[568,3321,812],{"className":3322},[811],[568,3324,3326],{"className":3325},[772],[568,3327,3329],{"className":3328,"style":3190},[776],[568,3330],{},[568,3332],{"className":3333,"style":1887},[825],[568,3335,1599],{"className":3336},[1891],[568,3338],{"className":3339,"style":1887},[825],[568,3341,3343,3346,3403,3406,3435,3438,3441,3444,3447,3450],{"className":3342},[602],[568,3344],{"className":3345,"style":1901},[606],[568,3347,3349,3352],{"className":3348},[753],[568,3350,703],{"className":3351,"style":1708},[753,757,1707],[568,3353,3355],{"className":3354},[763],[568,3356,3358,3395],{"className":3357},[767,768],[568,3359,3361,3392],{"className":3360},[772],[568,3362,3364,3378],{"className":3363,"style":1721},[776],[568,3365,3366,3369],{"style":1724},[568,3367],{"className":3368,"style":785},[784],[568,3370,3372],{"className":3371},[789,790,791,792],[568,3373,3375],{"className":3374},[611,792],[568,3376,736],{"className":3377},[611,792],[568,3379,3380,3383],{"style":1742},[568,3381],{"className":3382,"style":785},[784],[568,3384,3386],{"className":3385},[789,790,791,792],[568,3387,3389],{"className":3388},[611,792],[568,3390,1551],{"className":3391},[611,792],[568,3393,812],{"className":3394},[811],[568,3396,3398],{"className":3397},[772],[568,3399,3401],{"className":3400,"style":1957},[776],[568,3402],{},[568,3404],{"className":3405,"style":826},[825],[568,3407,3409,3412],{"className":3408},[611],[568,3410,717],{"className":3411},[611,612],[568,3413,3415],{"className":3414},[763],[568,3416,3418],{"className":3417},[767],[568,3419,3421],{"className":3420},[772],[568,3422,3424],{"className":3423,"style":2774},[776],[568,3425,3426,3429],{"style":2777},[568,3427],{"className":3428,"style":785},[784],[568,3430,3432],{"className":3431},[789,790,791,792],[568,3433,1554],{"className":3434},[611,792],[568,3436],{"className":3437,"style":826},[825],[568,3439,727],{"className":3440},[611,612],[568,3442,717],{"className":3443},[611,612],[568,3445],{"className":3446,"style":854},[825],[568,3448,732],{"className":3449},[858],[568,3451],{"className":3452,"style":854},[825],[568,3454,3456,3460,3602,3605,3608],{"className":3455},[602],[568,3457],{"className":3458,"style":3459},[606],"height:2.4em;vertical-align:-0.95em;",[568,3461,3463,3500,3503,3565],{"className":3462},[1994],[568,3464,3466],{"className":3465},[834],[568,3467,3469],{"className":3468},[2006,3149],[568,3470,3472,3492],{"className":3471},[767,768],[568,3473,3475,3489],{"className":3474},[772],[568,3476,3478],{"className":3477,"style":3159},[776],[568,3479,3480,3483],{"style":3162},[568,3481],{"className":3482,"style":3166},[784],[568,3484,3485],{"style":3169},[3171,3486,3487],{"xmlns":3173,"width":3174,"height":3175,"viewBox":3176},[3178,3488],{"d":3180},[568,3490,812],{"className":3491},[811],[568,3493,3495],{"className":3494},[772],[568,3496,3498],{"className":3497,"style":3190},[776],[568,3499],{},[568,3501,914],{"className":3502},[611],[568,3504,3506,3509,3562],{"className":3505},[611],[568,3507],{"className":3508},[834,2016],[568,3510,3512],{"className":3511},[1628],[568,3513,3515,3554],{"className":3514},[767,768],[568,3516,3518,3551],{"className":3517},[772],[568,3519,3521,3532,3540],{"className":3520,"style":2830},[776],[568,3522,3523,3526],{"style":2032},[568,3524],{"className":3525,"style":2036},[784],[568,3527,3529],{"className":3528},[611],[568,3530,2385],{"className":3531},[611],[568,3533,3534,3537],{"style":2045},[568,3535],{"className":3536,"style":2036},[784],[568,3538],{"className":3539,"style":2053},[2052],[568,3541,3542,3545],{"style":2056},[568,3543],{"className":3544,"style":2036},[784],[568,3546,3548],{"className":3547},[611],[568,3549,2543],{"className":3550},[611],[568,3552,812],{"className":3553},[811],[568,3555,3557],{"className":3556},[772],[568,3558,3560],{"className":3559,"style":2103},[776],[568,3561],{},[568,3563],{"className":3564},[841,2016],[568,3566,3568],{"className":3567},[841],[568,3569,3571],{"className":3570},[2006,3149],[568,3572,3574,3594],{"className":3573},[767,768],[568,3575,3577,3591],{"className":3576},[772],[568,3578,3580],{"className":3579,"style":3159},[776],[568,3581,3582,3585],{"style":3162},[568,3583],{"className":3584,"style":3166},[784],[568,3586,3587],{"style":3169},[3171,3588,3589],{"xmlns":3173,"width":3174,"height":3175,"viewBox":3176},[3178,3590],{"d":3180},[568,3592,812],{"className":3593},[811],[568,3595,3597],{"className":3596},[772],[568,3598,3600],{"className":3599,"style":3190},[776],[568,3601],{},[568,3603],{"className":3604,"style":1887},[825],[568,3606,1599],{"className":3607},[1891],[568,3609],{"className":3610,"style":1887},[825],[568,3612,3614,3617,3620,3623,3626],{"className":3613},[602],[568,3615],{"className":3616,"style":868},[606],[568,3618,2385],{"className":3619},[611],[568,3621],{"className":3622,"style":854},[825],[568,3624,732],{"className":3625},[858],[568,3627],{"className":3628,"style":854},[825],[568,3630,3632,3635,3638,3644],{"className":3631},[602],[568,3633],{"className":3634,"style":2381},[606],[568,3636,2385],{"className":3637},[611],[568,3639,3641],{"className":3640},[611],[568,3642,2393],{"className":3643},[2392],[568,3645,3647],{"className":3646},[611],"25",[559,3649,3651],{"id":3650},"typische-fehler","Typische Fehler",[679,3653,3654,3734,3737],{},[682,3655,3656,3657,3695,3696,872],{},"Bei einer Flächenberechnung nicht an den Nullstellen aufteilen. Im zweiten Beispiel erhält man dann ",[568,3658,3660,3674],{"className":3659},[571],[568,3661,3663],{"className":3662},[575],[577,3664,3665],{"xmlns":579},[581,3666,3667,3671],{},[584,3668,3669],{},[734,3670,2680],{},[591,3672,3673],{"encoding":593},"3{,}75",[568,3675,3677],{"className":3676,"ariaHidden":598},[597],[568,3678,3680,3683,3686,3692],{"className":3679},[602],[568,3681],{"className":3682,"style":2381},[606],[568,3684,1554],{"className":3685},[611],[568,3687,3689],{"className":3688},[611],[568,3690,2393],{"className":3691},[2392],[568,3693,2979],{"className":3694},[611]," statt ",[568,3697,3699,3713],{"className":3698},[571],[568,3700,3702],{"className":3701},[575],[577,3703,3704],{"xmlns":579},[581,3705,3706,3710],{},[584,3707,3708],{},[734,3709,3108],{},[591,3711,3712],{"encoding":593},"4{,}25",[568,3714,3716],{"className":3715,"ariaHidden":598},[597],[568,3717,3719,3722,3725,3731],{"className":3718},[602],[568,3720],{"className":3721,"style":2381},[606],[568,3723,2385],{"className":3724},[611],[568,3726,3728],{"className":3727},[611],[568,3729,2393],{"className":3730},[2392],[568,3732,3647],{"className":3733},[611],[682,3735,3736],{},"Teilintervalle verwenden, die nicht lückenlos aneinanderschließen: Die obere Grenze des ersten Integrals muss die untere Grenze des zweiten sein.",[682,3738,3739],{},"Beim Vertauschen der Grenzen das Vorzeichen nicht ändern.",{"title":3741,"searchDepth":3742,"depth":3742,"links":3743},"",2,[3744,3745,3746],{"id":561,"depth":3742,"text":562},{"id":1318,"depth":3742,"text":1319},{"id":3650,"depth":3742,"text":3651},[3748,3751,3754,3756,3759,3762,3764,3767],{"lhs":3749,"rhs":3750},"(v^3\u002F3 - u^3\u002F3) + (w^3\u002F3 - v^3\u002F3)","w^3\u002F3 - u^3\u002F3",{"lhs":3752,"rhs":3753},"u^3\u002F3 - v^3\u002F3","-(v^3\u002F3 - u^3\u002F3)",{"lhs":3755,"rhs":1551},"-(0^2)\u002F2 - (-((-2)^2)\u002F2)",{"lhs":3757,"rhs":3758},"3^2\u002F2 - 0^2\u002F2","4.5",{"lhs":3760,"rhs":3761},"2 + 4.5","6.5",{"lhs":3763,"rhs":3761},"round(sum(map(0:999, f(k) = abs(-2 + (k + 0.5) * 5 \u002F 1000))) * 5 \u002F 1000, 4)",{"lhs":3765,"rhs":3766},"2^4\u002F4 - (-1)^4\u002F4","3.75",{"lhs":3768,"rhs":3769},"abs(0^4\u002F4 - (-1)^4\u002F4) + (2^4\u002F4 - 0^4\u002F4)","4.25","f \\text{ stetig auf einem Intervall, das } a, b \\text{ und } c \\text{ enthält}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">stetig auf einem Intervall, das\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">und\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">c\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">enthält\u003C\u002Fspan>",null,"md",{"caption":3775,"x":3776,"y":3779,"unit":3782,"ticks":3783,"axes":3785,"items":3786},"Die Fläche unter f von a bis c setzt sich aus den Flächen von a bis b und von b bis c zusammen",[3777,3778],-0.4,4.6,[3780,3781],-0.7,3.4,52,[3784,3784],10,true,[3787,3793,3801,3806,3810,3813,3815],{"type":3788,"expr":3789,"domain":3790},"area","0.25*(x - 1.5)^2 + 1",[3791,3792],0.5,4,{"type":3794,"from":3795,"to":3798,"style":3800},"segment",[3796,3797],2.2,0,[3796,3799],1.1225,"dashed",{"type":3802,"expr":3789,"domain":3803},"function",[3804,3805],0.1,4.4,{"type":3807,"at":3808,"text":710},"label",[3792,3809],3.05,{"type":3807,"at":3811,"text":589},[3791,3812],-0.35,{"type":3807,"at":3814,"text":658},[3796,3812],{"type":3807,"at":3816,"text":628},[3792,3812],"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 260 213.2\" width=\"260\" height=\"213.2\" role=\"img\" aria-label=\"Die Fläche unter f von a bis c setzt sich aus den Flächen von a bis b und von b bis c zusammen\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-integral-additivity-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-integral-additivity-clip\">\u003Crect x=\"0\" y=\"0\" width=\"260\" height=\"213.2\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cline x1=\"0\" y1=\"176.8\" x2=\"260\" y2=\"176.8\" class=\"fig-axis\" marker-end=\"url(#fig-integral-additivity-arrow)\"\u002F>\u003Cline x1=\"20.8\" y1=\"213.2\" x2=\"20.8\" y2=\"0\" class=\"fig-axis\" marker-end=\"url(#fig-integral-additivity-arrow)\"\u002F>\u003Ctext x=\"254\" y=\"164.8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">x\u003C\u002Ftext>\u003Ctext x=\"32.8\" y=\"8\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">y\u003C\u002Ftext>\u003Cpolygon points=\"46.8,111.8 48.32,112.55 49.83,113.27 51.35,113.98 52.87,114.66 54.38,115.32 55.9,115.95 57.42,116.57 58.93,117.16 60.45,117.73 61.97,118.28 63.48,118.8 65,119.31 66.52,119.79 68.03,120.25 69.55,120.69 71.07,121.1 72.58,121.5 74.1,121.87 75.62,122.22 77.13,122.54 78.65,122.85 80.17,123.13 81.68,123.39 83.2,123.63 84.72,123.85 86.23,124.04 87.75,124.21 89.27,124.36 90.78,124.49 92.3,124.6 93.82,124.68 95.33,124.74 96.85,124.78 98.37,124.8 99.88,124.79 101.4,124.77 102.92,124.72 104.43,124.65 105.95,124.55 107.47,124.44 108.98,124.3 110.5,124.14 112.02,123.96 113.53,123.76 115.05,123.53 116.57,123.28 118.08,123.01 119.6,122.72 121.12,122.41 122.63,122.07 124.15,121.71 125.67,121.33 127.18,120.93 128.7,120.5 130.22,120.05 131.73,119.59 133.25,119.09 134.77,118.58 136.28,118.05 137.8,117.49 139.32,116.91 140.83,116.31 142.35,115.68 143.87,115.04 145.38,114.37 146.9,113.68 148.42,112.96 149.93,112.23 151.45,111.47 152.97,110.69 154.48,109.89 156,109.07 157.52,108.22 159.03,107.36 160.55,106.47 162.07,105.56 163.58,104.62 165.1,103.67 166.62,102.69 168.13,101.69 169.65,100.67 171.17,99.62 172.68,98.56 174.2,97.47 175.72,96.36 177.23,95.22 178.75,94.07 180.27,92.89 181.78,91.69 183.3,90.47 184.82,89.23 186.33,87.96 187.85,86.68 189.37,85.37 190.88,84.03 192.4,82.68 193.92,81.3 195.43,79.91 196.95,78.49 198.47,77.04 199.98,75.58 201.5,74.09 203.02,72.58 204.53,71.05 206.05,69.5 207.57,67.92 209.08,66.33 210.6,64.71 212.12,63.07 213.63,61.4 215.15,59.72 216.67,58.01 218.18,56.28 219.7,54.53 221.22,52.75 222.73,50.96 224.25,49.14 225.77,47.3 227.28,45.43 228.8,43.55 228.8,176.8 227.28,176.8 225.77,176.8 224.25,176.8 222.73,176.8 221.22,176.8 219.7,176.8 218.18,176.8 216.67,176.8 215.15,176.8 213.63,176.8 212.12,176.8 210.6,176.8 209.08,176.8 207.57,176.8 206.05,176.8 204.53,176.8 203.02,176.8 201.5,176.8 199.98,176.8 198.47,176.8 196.95,176.8 195.43,176.8 193.92,176.8 192.4,176.8 190.88,176.8 189.37,176.8 187.85,176.8 186.33,176.8 184.82,176.8 183.3,176.8 181.78,176.8 180.27,176.8 178.75,176.8 177.23,176.8 175.72,176.8 174.2,176.8 172.68,176.8 171.17,176.8 169.65,176.8 168.13,176.8 166.62,176.8 165.1,176.8 163.58,176.8 162.07,176.8 160.55,176.8 159.03,176.8 157.52,176.8 156,176.8 154.48,176.8 152.97,176.8 151.45,176.8 149.93,176.8 148.42,176.8 146.9,176.8 145.38,176.8 143.87,176.8 142.35,176.8 140.83,176.8 139.32,176.8 137.8,176.8 136.28,176.8 134.77,176.8 133.25,176.8 131.73,176.8 130.22,176.8 128.7,176.8 127.18,176.8 125.67,176.8 124.15,176.8 122.63,176.8 121.12,176.8 119.6,176.8 118.08,176.8 116.57,176.8 115.05,176.8 113.53,176.8 112.02,176.8 110.5,176.8 108.98,176.8 107.47,176.8 105.95,176.8 104.43,176.8 102.92,176.8 101.4,176.8 99.88,176.8 98.37,176.8 96.85,176.8 95.33,176.8 93.82,176.8 92.3,176.8 90.78,176.8 89.27,176.8 87.75,176.8 86.23,176.8 84.72,176.8 83.2,176.8 81.68,176.8 80.17,176.8 78.65,176.8 77.13,176.8 75.62,176.8 74.1,176.8 72.58,176.8 71.07,176.8 69.55,176.8 68.03,176.8 66.52,176.8 65,176.8 63.48,176.8 61.97,176.8 60.45,176.8 58.93,176.8 57.42,176.8 55.9,176.8 54.38,176.8 52.87,176.8 51.35,176.8 49.83,176.8 48.32,176.8 46.8,176.8\" class=\"fig-area\" clip-path=\"url(#fig-integral-additivity-clip)\"\u002F>\u003Cline x1=\"135.2\" y1=\"176.8\" x2=\"135.2\" y2=\"118.43\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 26 99.32 L 26.93 99.97 L 27.86 100.61 L 28.8 101.24 L 29.73 101.86 L 30.66 102.48 L 31.59 103.08 L 32.52 103.68 L 33.45 104.27 L 34.39 104.85 L 35.32 105.42 L 36.25 105.99 L 37.18 106.55 L 38.11 107.09 L 39.04 107.63 L 39.98 108.16 L 40.91 108.69 L 41.84 109.2 L 42.77 109.71 L 43.7 110.2 L 44.63 110.69 L 45.57 111.18 L 46.5 111.65 L 47.43 112.11 L 48.36 112.57 L 49.29 113.02 L 50.22 113.46 L 51.16 113.89 L 52.09 114.31 L 53.02 114.72 L 53.95 115.13 L 54.88 115.53 L 55.81 115.92 L 56.75 116.3 L 57.68 116.67 L 58.61 117.03 L 59.54 117.39 L 60.47 117.74 L 61.4 118.08 L 62.34 118.41 L 63.27 118.73 L 64.2 119.04 L 65.13 119.35 L 66.06 119.65 L 66.99 119.94 L 67.93 120.22 L 68.86 120.49 L 69.79 120.75 L 70.72 121.01 L 71.65 121.26 L 72.58 121.5 L 73.52 121.73 L 74.45 121.95 L 75.38 122.16 L 76.31 122.37 L 77.24 122.57 L 78.17 122.75 L 79.11 122.94 L 80.04 123.11 L 80.97 123.27 L 81.9 123.43 L 82.83 123.57 L 83.76 123.71 L 84.7 123.84 L 85.63 123.97 L 86.56 124.08 L 87.49 124.19 L 88.42 124.28 L 89.35 124.37 L 90.29 124.45 L 91.22 124.52 L 92.15 124.59 L 93.08 124.64 L 94.01 124.69 L 94.94 124.73 L 95.88 124.76 L 96.81 124.78 L 97.74 124.79 L 98.67 124.8 L 99.6 124.8 L 100.53 124.79 L 101.47 124.77 L 102.4 124.74 L 103.33 124.7 L 104.26 124.66 L 105.19 124.6 L 106.12 124.54 L 107.06 124.47 L 107.99 124.39 L 108.92 124.31 L 109.85 124.21 L 110.78 124.11 L 111.71 124 L 112.65 123.88 L 113.58 123.75 L 114.51 123.61 L 115.44 123.47 L 116.37 123.32 L 117.3 123.15 L 118.24 122.98 L 119.17 122.81 L 120.1 122.62 L 121.03 122.42 L 121.96 122.22 L 122.89 122.01 L 123.83 121.79 L 124.76 121.56 L 125.69 121.32 L 126.62 121.08 L 127.55 120.83 L 128.48 120.56 L 129.42 120.29 L 130.35 120.02 L 131.28 119.73 L 132.21 119.43 L 133.14 119.13 L 134.07 118.82 L 135.01 118.5 L 135.94 118.17 L 136.87 117.83 L 137.8 117.49 L 138.73 117.13 L 139.66 116.77 L 140.6 116.4 L 141.53 116.02 L 142.46 115.64 L 143.39 115.24 L 144.32 114.84 L 145.25 114.43 L 146.19 114.01 L 147.12 113.58 L 148.05 113.14 L 148.98 112.69 L 149.91 112.24 L 150.84 111.78 L 151.78 111.31 L 152.71 110.83 L 153.64 110.34 L 154.57 109.85 L 155.5 109.34 L 156.43 108.83 L 157.37 108.31 L 158.3 107.78 L 159.23 107.24 L 160.16 106.7 L 161.09 106.14 L 162.02 105.58 L 162.96 105.01 L 163.89 104.43 L 164.82 103.85 L 165.75 103.25 L 166.68 102.65 L 167.61 102.03 L 168.55 101.41 L 169.48 100.78 L 170.41 100.15 L 171.34 99.5 L 172.27 98.85 L 173.2 98.19 L 174.14 97.51 L 175.07 96.84 L 176 96.15 L 176.93 95.45 L 177.86 94.75 L 178.79 94.04 L 179.73 93.32 L 180.66 92.59 L 181.59 91.85 L 182.52 91.1 L 183.45 90.35 L 184.38 89.59 L 185.32 88.82 L 186.25 88.04 L 187.18 87.25 L 188.11 86.45 L 189.04 85.65 L 189.97 84.84 L 190.91 84.01 L 191.84 83.19 L 192.77 82.35 L 193.7 81.5 L 194.63 80.65 L 195.56 79.78 L 196.5 78.91 L 197.43 78.03 L 198.36 77.15 L 199.29 76.25 L 200.22 75.35 L 201.15 74.43 L 202.09 73.51 L 203.02 72.58 L 203.95 71.65 L 204.88 70.7 L 205.81 69.74 L 206.74 68.78 L 207.68 67.81 L 208.61 66.83 L 209.54 65.84 L 210.47 64.85 L 211.4 63.84 L 212.33 62.83 L 213.27 61.81 L 214.2 60.78 L 215.13 59.74 L 216.06 58.69 L 216.99 57.64 L 217.92 56.58 L 218.86 55.51 L 219.79 54.43 L 220.72 53.34 L 221.65 52.24 L 222.58 51.14 L 223.51 50.02 L 224.45 48.9 L 225.38 47.77 L 226.31 46.63 L 227.24 45.49 L 228.17 44.33 L 229.1 43.17 L 230.04 42 L 230.97 40.82 L 231.9 39.63 L 232.83 38.43 L 233.76 37.23 L 234.69 36.02 L 235.63 34.79 L 236.56 33.56 L 237.49 32.33 L 238.42 31.08 L 239.35 29.83 L 240.28 28.56 L 241.22 27.29 L 242.15 26.01 L 243.08 24.72 L 244.01 23.43 L 244.94 22.12 L 245.87 20.81 L 246.81 19.49 L 247.74 18.16 L 248.67 16.82 L 249.6 15.47\" class=\"fig-main fig-graph\" clip-path=\"url(#fig-integral-additivity-clip)\"\u002F>\u003Ctext x=\"228.8\" y=\"18.2\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">f\u003C\u002Ftext>\u003Ctext x=\"46.8\" y=\"195\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"135.2\" y=\"195\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">b\u003C\u002Ftext>\u003Ctext x=\"228.8\" y=\"195\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">c\u003C\u002Ftext>\u003C\u002Fsvg>","integral-additivity","\\int_a^b f(x)\\,dx + \\int_b^c f(x)\\,dx = \\int_a^c f(x)\\,dx","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsubsup>\u003Cmo>∫\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmsubsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmsubsup>\u003Cmo>∫\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmsubsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsubsup>\u003Cmo>∫\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmsubsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\int_a^b f(x)\\,dx + \\int_b^c f(x)\\,dx = \\int_a^c f(x)\\,dx\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.511em;vertical-align:-0.9119em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.599em;\">\u003Cspan style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8129em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9119em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.3262em;vertical-align:-0.9119em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4143em;\">\u003Cspan style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8129em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9119em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.3262em;vertical-align:-0.9119em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4143em;\">\u003Cspan style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8129em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9119em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintervalladditivitaet",[],[3826,3827,3828],"fundamental-theorem","integral-linearity","area-between-curves",{"title":548,"description":3741},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintervalladditivitaet","Ein Integral lässt sich an einer Zwischenstelle in zwei Integrale aufteilen, deren Werte sich addieren.",[3833,3834,3835,3836],"integral","intervall","integrationsgrenzen","aufteilen",[3838,3841,3845],{"symbol":710,"meaning":3839,"symbolHtml":3840},"Integrand","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3842,"meaning":3843,"symbolHtml":3844},"a, c","äußere Integrationsgrenzen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, c\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":658,"meaning":3846,"symbolHtml":3847},"Zwischenstelle, an der das Integral aufgeteilt wird","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","D-2gL4PKKJuCAutwpGFliAksNgNK8896nlwzU9cTXHA",[3850,3853,3856],{"stem":3851,"title":3852,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Ffaktor-und-summenregel-integral","Faktor- und Summenregel der Integration",{"stem":3854,"title":3855,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fflaeche-zwischen-zwei-graphen","Fläche zwischen zwei Graphen",{"stem":3857,"title":3858,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fhauptsatz-der-differential-und-integralrechnung","Hauptsatz der Differential- und Integralrechnung",1793824282352]