[{"data":1,"prerenderedAt":3234},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegral-kosinus":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegral-kosinus":3221},[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":556,"category":101,"checks":3176,"conditions":3188,"conditionsHtml":3189,"deprecated":3190,"description":3170,"extension":3191,"figure":3190,"figureCaption":3190,"figureHtml":3190,"formulaId":3192,"latex":3193,"latexHtml":3194,"level":3195,"meta":3196,"navigation":3197,"path":3198,"redirectFrom":3199,"related":3200,"seo":3205,"stem":3206,"subject":578,"summary":3207,"tags":3208,"variables":3213,"__hash__":3220},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegral-kosinus.md","Integral des Kosinus",[550,551,552,553,554,555],"Stammfunktion cos","cos x integrieren","Integral cos x","Kosinus aufleiten","Stammfunktion Kosinus","Cosinus integrieren",{"type":557,"value":558,"toc":3169},"minimark",[559,564,718,754,907,911,1404,2061,2123,2336,2541,2545],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,631,632,673,674,712,713,717],"p",{},"Die Ableitung von ",[569,570,573,603],"span",{"className":571},[572],"katex",[569,574,577],{"className":575},[576],"katex-mathml",[578,579,581],"math",{"xmlns":580},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[582,583,584,598],"semantics",{},[585,586,587,591,595],"mrow",{},[588,589,590],"mi",{},"sin",[592,593,594],"mo",{},"⁡",[588,596,597],{},"x",[599,600,602],"annotation",{"encoding":601},"application\u002Fx-tex","\\sin x",[569,604,608],{"className":605,"ariaHidden":607},[606],"katex-html","true",[569,609,612,617,621,626],{"className":610},[611],"base",[569,613],{"className":614,"style":616},[615],"strut","height:0.6679em;",[569,618,590],{"className":619},[620],"mop",[569,622],{"className":623,"style":625},[624],"mspace","margin-right:0.1667em;",[569,627,597],{"className":628},[629,630],"mord","mathnormal"," ist ",[569,633,635,654],{"className":634},[572],[569,636,638],{"className":637},[576],[578,639,640],{"xmlns":580},[582,641,642,651],{},[585,643,644,647,649],{},[588,645,646],{},"cos",[592,648,594],{},[588,650,597],{},[599,652,653],{"encoding":601},"\\cos x",[569,655,657],{"className":656,"ariaHidden":607},[606],[569,658,660,664,667,670],{"className":659},[611],[569,661],{"className":662,"style":663},[615],"height:0.4306em;",[569,665,646],{"className":666},[620],[569,668],{"className":669,"style":625},[624],[569,671,597],{"className":672},[629,630],". Deshalb ist ",[569,675,677,694],{"className":676},[572],[569,678,680],{"className":679},[576],[578,681,682],{"xmlns":580},[582,683,684,692],{},[585,685,686,688,690],{},[588,687,590],{},[592,689,594],{},[588,691,597],{},[599,693,602],{"encoding":601},[569,695,697],{"className":696,"ariaHidden":607},[606],[569,698,700,703,706,709],{"className":699},[611],[569,701],{"className":702,"style":616},[615],[569,704,590],{"className":705},[620],[569,707],{"className":708,"style":625},[624],[569,710,597],{"className":711},[629,630]," eine Stammfunktion des Kosinus. Anders als beim Sinus entsteht hier ",[714,715,716],"strong",{},"kein"," Minuszeichen.",[565,719,720,721,749,750,753],{},"Die Formel gilt nur, wenn ",[569,722,724,737],{"className":723},[572],[569,725,727],{"className":726},[576],[578,728,729],{"xmlns":580},[582,730,731,735],{},[585,732,733],{},[588,734,597],{},[599,736,597],{"encoding":601},[569,738,740],{"className":739,"ariaHidden":607},[606],[569,741,743,746],{"className":742},[611],[569,744],{"className":745,"style":663},[615],[569,747,597],{"className":748},[629,630]," im ",[714,751,752],{},"Bogenmaß"," gemessen wird.",[565,755,756,757,906],{},"Merkhilfe für die Vorzeichen: Beim Ableiten geht es im Kreis ",[569,758,760,806],{"className":759},[572],[569,761,763],{"className":762},[576],[578,764,765],{"xmlns":580},[582,766,767,803],{},[585,768,769,771,773,776,778,780,782,785,787,789,791,793,795,797,799,801],{},[588,770,590],{},[592,772,594],{},[592,774,775],{},"→",[588,777,646],{},[592,779,594],{},[592,781,775],{},[592,783,784],{},"−",[588,786,590],{},[592,788,594],{},[592,790,775],{},[592,792,784],{},[588,794,646],{},[592,796,594],{},[592,798,775],{},[588,800,590],{},[592,802,594],{},[599,804,805],{"encoding":601},"\\sin \\to \\cos \\to -\\sin \\to -\\cos \\to \\sin",[569,807,809,829,847,872,897],{"className":808,"ariaHidden":607},[606],[569,810,812,815,818,822,826],{"className":811},[611],[569,813],{"className":814,"style":616},[615],[569,816,590],{"className":817},[620],[569,819],{"className":820,"style":821},[624],"margin-right:0.2778em;",[569,823,775],{"className":824},[825],"mrel",[569,827],{"className":828,"style":821},[624],[569,830,832,835,838,841,844],{"className":831},[611],[569,833],{"className":834,"style":663},[615],[569,836,646],{"className":837},[620],[569,839],{"className":840,"style":821},[624],[569,842,775],{"className":843},[825],[569,845],{"className":846,"style":821},[624],[569,848,850,854,857,860,863,866,869],{"className":849},[611],[569,851],{"className":852,"style":853},[615],"height:0.7512em;vertical-align:-0.0833em;",[569,855,784],{"className":856},[629],[569,858],{"className":859,"style":625},[624],[569,861,590],{"className":862},[620],[569,864],{"className":865,"style":821},[624],[569,867,775],{"className":868},[825],[569,870],{"className":871,"style":821},[624],[569,873,875,879,882,885,888,891,894],{"className":874},[611],[569,876],{"className":877,"style":878},[615],"height:0.6667em;vertical-align:-0.0833em;",[569,880,784],{"className":881},[629],[569,883],{"className":884,"style":625},[624],[569,886,646],{"className":887},[620],[569,889],{"className":890,"style":821},[624],[569,892,775],{"className":893},[825],[569,895],{"className":896,"style":821},[624],[569,898,900,903],{"className":899},[611],[569,901],{"className":902,"style":616},[615],[569,904,590],{"className":905},[620],", beim Integrieren in umgekehrter Richtung.",[560,908,910],{"id":909},"beispiele","Beispiele",[569,912,915],{"className":913},[914],"katex-display",[569,916,918,1005],{"className":917},[572],[569,919,921],{"className":920},[576],[578,922,924],{"xmlns":580,"display":923},"block",[582,925,926,1002],{},[585,927,928,947,949,951,953,957,960,962,965,989,991,994,996,998,1000],{},[929,930,931,934,938],"msubsup",{},[592,932,933],{},"∫",[935,936,937],"mn",{},"0",[939,940,941,944],"mfrac",{},[588,942,943],{},"π",[935,945,946],{},"2",[588,948,646],{},[592,950,594],{},[588,952,597],{},[954,955,956],"mtext",{}," ",[588,958,959],{},"d",[588,961,597],{},[592,963,964],{},"=",[929,966,967,981,983],{},[585,968,969,972,974,976,978],{},[592,970,971],{"fence":607},"[",[588,973,590],{},[592,975,594],{},[588,977,597],{},[592,979,980],{"fence":607},"]",[935,982,937],{},[939,984,985,987],{},[588,986,943],{},[935,988,946],{},[592,990,964],{},[935,992,993],{},"1",[592,995,784],{},[935,997,937],{},[592,999,964],{},[935,1001,993],{},[599,1003,1004],{"encoding":601},"\\int_0^{\\frac{\\pi}{2}} \\cos x \\, dx = \\left[\\sin x\\right]_0^{\\frac{\\pi}{2}} = 1 - 0 = 1",[569,1006,1008,1198,1355,1376,1395],{"className":1007,"ariaHidden":607},[606],[569,1009,1011,1015,1168,1171,1174,1177,1180,1183,1186,1189,1192,1195],{"className":1010},[611],[569,1012],{"className":1013,"style":1014},[615],"height:2.5089em;vertical-align:-0.9119em;",[569,1016,1018,1024],{"className":1017},[620],[569,1019,933],{"className":1020,"style":1023},[620,1021,1022],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[569,1025,1028],{"className":1026},[1027],"msupsub",[569,1029,1033,1159],{"className":1030},[1031,1032],"vlist-t","vlist-t2",[569,1034,1037,1156],{"className":1035},[1036],"vlist-r",[569,1038,1042,1060],{"className":1039,"style":1041},[1040],"vlist","height:1.597em;",[569,1043,1045,1050],{"style":1044},"top:-2.088em;margin-left:-0.4445em;margin-right:0.05em;",[569,1046],{"className":1047,"style":1049},[1048],"pstrut","height:3em;",[569,1051,1057],{"className":1052},[1053,1054,1055,1056],"sizing","reset-size6","size3","mtight",[569,1058,937],{"className":1059},[629,1056],[569,1061,1063,1066],{"style":1062},"top:-4.1129em;margin-right:0.05em;",[569,1064],{"className":1065,"style":1049},[1048],[569,1067,1069],{"className":1068},[1053,1054,1055,1056],[569,1070,1072],{"className":1071},[629,1056],[569,1073,1075,1082,1152],{"className":1074},[629,1056],[569,1076],{"className":1077},[1078,1079,1053,1080,1081],"mopen","nulldelimiter","reset-size3","size6",[569,1083,1085],{"className":1084},[939],[569,1086,1088,1143],{"className":1087},[1031,1032],[569,1089,1091,1138],{"className":1090},[1036],[569,1092,1095,1111,1122],{"className":1093,"style":1094},[1040],"height:0.6915em;",[569,1096,1098,1101],{"style":1097},"top:-2.656em;",[569,1099],{"className":1100,"style":1049},[1048],[569,1102,1105],{"className":1103},[1053,1080,1104,1056],"size1",[569,1106,1108],{"className":1107},[629,1056],[569,1109,946],{"className":1110},[629,1056],[569,1112,1114,1117],{"style":1113},"top:-3.2255em;",[569,1115],{"className":1116,"style":1049},[1048],[569,1118],{"className":1119,"style":1121},[1120,1056],"frac-line","border-bottom-width:0.049em;",[569,1123,1125,1128],{"style":1124},"top:-3.384em;",[569,1126],{"className":1127,"style":1049},[1048],[569,1129,1131],{"className":1130},[1053,1080,1104,1056],[569,1132,1134],{"className":1133},[629,1056],[569,1135,943],{"className":1136,"style":1137},[629,630,1056],"margin-right:0.0359em;",[569,1139,1142],{"className":1140},[1141],"vlist-s","​",[569,1144,1146],{"className":1145},[1036],[569,1147,1150],{"className":1148,"style":1149},[1040],"height:0.344em;",[569,1151],{},[569,1153],{"className":1154},[1155,1079,1053,1080,1081],"mclose",[569,1157,1142],{"className":1158},[1141],[569,1160,1162],{"className":1161},[1036],[569,1163,1166],{"className":1164,"style":1165},[1040],"height:0.9119em;",[569,1167],{},[569,1169],{"className":1170,"style":625},[624],[569,1172,646],{"className":1173},[620],[569,1175],{"className":1176,"style":625},[624],[569,1178,597],{"className":1179},[629,630],[569,1181],{"className":1182,"style":625},[624],[569,1184,959],{"className":1185},[629,630],[569,1187,597],{"className":1188},[629,630],[569,1190],{"className":1191,"style":821},[624],[569,1193,964],{"className":1194},[825],[569,1196],{"className":1197,"style":821},[624],[569,1199,1201,1205,1346,1349,1352],{"className":1200},[611],[569,1202],{"className":1203,"style":1204},[615],"height:1.336em;vertical-align:-0.2663em;",[569,1206,1209,1229],{"className":1207},[1208],"minner",[569,1210,1212,1217,1220,1223,1226],{"className":1211},[1208],[569,1213,971],{"className":1214,"style":1216},[1078,1215],"delimcenter","top:0em;",[569,1218,590],{"className":1219},[620],[569,1221],{"className":1222,"style":625},[624],[569,1224,597],{"className":1225},[629,630],[569,1227,980],{"className":1228,"style":1216},[1155,1215],[569,1230,1232],{"className":1231},[1027],[569,1233,1235,1337],{"className":1234},[1031,1032],[569,1236,1238,1334],{"className":1237},[1036],[569,1239,1242,1254],{"className":1240,"style":1241},[1040],"height:1.0697em;",[569,1243,1245,1248],{"style":1244},"top:-2.7337em;margin-right:0.05em;",[569,1246],{"className":1247,"style":1049},[1048],[569,1249,1251],{"className":1250},[1053,1054,1055,1056],[569,1252,937],{"className":1253},[629,1056],[569,1255,1257,1260],{"style":1256},"top:-3.5856em;margin-right:0.05em;",[569,1258],{"className":1259,"style":1049},[1048],[569,1261,1263],{"className":1262},[1053,1054,1055,1056],[569,1264,1266],{"className":1265},[629,1056],[569,1267,1269,1272,1331],{"className":1268},[629,1056],[569,1270],{"className":1271},[1078,1079,1053,1080,1081],[569,1273,1275],{"className":1274},[939],[569,1276,1278,1323],{"className":1277},[1031,1032],[569,1279,1281,1320],{"className":1280},[1036],[569,1282,1284,1298,1306],{"className":1283,"style":1094},[1040],[569,1285,1286,1289],{"style":1097},[569,1287],{"className":1288,"style":1049},[1048],[569,1290,1292],{"className":1291},[1053,1080,1104,1056],[569,1293,1295],{"className":1294},[629,1056],[569,1296,946],{"className":1297},[629,1056],[569,1299,1300,1303],{"style":1113},[569,1301],{"className":1302,"style":1049},[1048],[569,1304],{"className":1305,"style":1121},[1120,1056],[569,1307,1308,1311],{"style":1124},[569,1309],{"className":1310,"style":1049},[1048],[569,1312,1314],{"className":1313},[1053,1080,1104,1056],[569,1315,1317],{"className":1316},[629,1056],[569,1318,943],{"className":1319,"style":1137},[629,630,1056],[569,1321,1142],{"className":1322},[1141],[569,1324,1326],{"className":1325},[1036],[569,1327,1329],{"className":1328,"style":1149},[1040],[569,1330],{},[569,1332],{"className":1333},[1155,1079,1053,1080,1081],[569,1335,1142],{"className":1336},[1141],[569,1338,1340],{"className":1339},[1036],[569,1341,1344],{"className":1342,"style":1343},[1040],"height:0.2663em;",[569,1345],{},[569,1347],{"className":1348,"style":821},[624],[569,1350,964],{"className":1351},[825],[569,1353],{"className":1354,"style":821},[624],[569,1356,1358,1362,1365,1369,1373],{"className":1357},[611],[569,1359],{"className":1360,"style":1361},[615],"height:0.7278em;vertical-align:-0.0833em;",[569,1363,993],{"className":1364},[629],[569,1366],{"className":1367,"style":1368},[624],"margin-right:0.2222em;",[569,1370,784],{"className":1371},[1372],"mbin",[569,1374],{"className":1375,"style":1368},[624],[569,1377,1379,1383,1386,1389,1392],{"className":1378},[611],[569,1380],{"className":1381,"style":1382},[615],"height:0.6444em;",[569,1384,937],{"className":1385},[629],[569,1387],{"className":1388,"style":821},[624],[569,1390,964],{"className":1391},[825],[569,1393],{"className":1394,"style":821},[624],[569,1396,1398,1401],{"className":1397},[611],[569,1399],{"className":1400,"style":1382},[615],[569,1402,993],{"className":1403},[629],[569,1405,1407],{"className":1406},[914],[569,1408,1410,1495],{"className":1409},[572],[569,1411,1413],{"className":1412},[576],[578,1414,1415],{"xmlns":580,"display":923},[582,1416,1417,1492],{},[585,1418,1419,1436,1438,1440,1442,1444,1446,1448,1450,1452,1454,1460,1462,1464,1466,1472,1474,1476,1478,1484,1486],{},[929,1420,1421,1423,1430],{},[592,1422,933],{},[939,1424,1425,1427],{},[588,1426,943],{},[935,1428,1429],{},"6",[939,1431,1432,1434],{},[588,1433,943],{},[935,1435,946],{},[588,1437,646],{},[592,1439,594],{},[588,1441,597],{},[954,1443,956],{},[588,1445,959],{},[588,1447,597],{},[592,1449,964],{},[588,1451,590],{},[592,1453,594],{},[939,1455,1456,1458],{},[588,1457,943],{},[935,1459,946],{},[592,1461,784],{},[588,1463,590],{},[592,1465,594],{},[939,1467,1468,1470],{},[588,1469,943],{},[935,1471,1429],{},[592,1473,964],{},[935,1475,993],{},[592,1477,784],{},[939,1479,1480,1482],{},[935,1481,993],{},[935,1483,946],{},[592,1485,964],{},[939,1487,1488,1490],{},[935,1489,993],{},[935,1491,946],{},[599,1493,1494],{"encoding":601},"\\int_{\\frac{\\pi}{6}}^{\\frac{\\pi}{2}} \\cos x \\, dx = \\sin \\frac{\\pi}{2} - \\sin \\frac{\\pi}{6} = 1 - \\frac{1}{2} = \\frac{1}{2}",[569,1496,1498,1723,1813,1896,1914,1993],{"className":1497,"ariaHidden":607},[606],[569,1499,1501,1505,1693,1696,1699,1702,1705,1708,1711,1714,1717,1720],{"className":1500},[611],[569,1502],{"className":1503,"style":1504},[615],"height:2.7497em;vertical-align:-1.1527em;",[569,1506,1508,1511],{"className":1507},[620],[569,1509,933],{"className":1510,"style":1023},[620,1021,1022],[569,1512,1514],{"className":1513},[1027],[569,1515,1517,1684],{"className":1516},[1031,1032],[569,1518,1520,1681],{"className":1519},[1036],[569,1521,1523,1602],{"className":1522,"style":1041},[1040],[569,1524,1525,1528],{"style":1044},[569,1526],{"className":1527,"style":1049},[1048],[569,1529,1531],{"className":1530},[1053,1054,1055,1056],[569,1532,1534],{"className":1533},[629,1056],[569,1535,1537,1540,1599],{"className":1536},[629,1056],[569,1538],{"className":1539},[1078,1079,1053,1080,1081],[569,1541,1543],{"className":1542},[939],[569,1544,1546,1591],{"className":1545},[1031,1032],[569,1547,1549,1588],{"className":1548},[1036],[569,1550,1552,1566,1574],{"className":1551,"style":1094},[1040],[569,1553,1554,1557],{"style":1097},[569,1555],{"className":1556,"style":1049},[1048],[569,1558,1560],{"className":1559},[1053,1080,1104,1056],[569,1561,1563],{"className":1562},[629,1056],[569,1564,1429],{"className":1565},[629,1056],[569,1567,1568,1571],{"style":1113},[569,1569],{"className":1570,"style":1049},[1048],[569,1572],{"className":1573,"style":1121},[1120,1056],[569,1575,1576,1579],{"style":1124},[569,1577],{"className":1578,"style":1049},[1048],[569,1580,1582],{"className":1581},[1053,1080,1104,1056],[569,1583,1585],{"className":1584},[629,1056],[569,1586,943],{"className":1587,"style":1137},[629,630,1056],[569,1589,1142],{"className":1590},[1141],[569,1592,1594],{"className":1593},[1036],[569,1595,1597],{"className":1596,"style":1149},[1040],[569,1598],{},[569,1600],{"className":1601},[1155,1079,1053,1080,1081],[569,1603,1604,1607],{"style":1062},[569,1605],{"className":1606,"style":1049},[1048],[569,1608,1610],{"className":1609},[1053,1054,1055,1056],[569,1611,1613],{"className":1612},[629,1056],[569,1614,1616,1619,1678],{"className":1615},[629,1056],[569,1617],{"className":1618},[1078,1079,1053,1080,1081],[569,1620,1622],{"className":1621},[939],[569,1623,1625,1670],{"className":1624},[1031,1032],[569,1626,1628,1667],{"className":1627},[1036],[569,1629,1631,1645,1653],{"className":1630,"style":1094},[1040],[569,1632,1633,1636],{"style":1097},[569,1634],{"className":1635,"style":1049},[1048],[569,1637,1639],{"className":1638},[1053,1080,1104,1056],[569,1640,1642],{"className":1641},[629,1056],[569,1643,946],{"className":1644},[629,1056],[569,1646,1647,1650],{"style":1113},[569,1648],{"className":1649,"style":1049},[1048],[569,1651],{"className":1652,"style":1121},[1120,1056],[569,1654,1655,1658],{"style":1124},[569,1656],{"className":1657,"style":1049},[1048],[569,1659,1661],{"className":1660},[1053,1080,1104,1056],[569,1662,1664],{"className":1663},[629,1056],[569,1665,943],{"className":1666,"style":1137},[629,630,1056],[569,1668,1142],{"className":1669},[1141],[569,1671,1673],{"className":1672},[1036],[569,1674,1676],{"className":1675,"style":1149},[1040],[569,1677],{},[569,1679],{"className":1680},[1155,1079,1053,1080,1081],[569,1682,1142],{"className":1683},[1141],[569,1685,1687],{"className":1686},[1036],[569,1688,1691],{"className":1689,"style":1690},[1040],"height:1.1527em;",[569,1692],{},[569,1694],{"className":1695,"style":625},[624],[569,1697,646],{"className":1698},[620],[569,1700],{"className":1701,"style":625},[624],[569,1703,597],{"className":1704},[629,630],[569,1706],{"className":1707,"style":625},[624],[569,1709,959],{"className":1710},[629,630],[569,1712,597],{"className":1713},[629,630],[569,1715],{"className":1716,"style":821},[624],[569,1718,964],{"className":1719},[825],[569,1721],{"className":1722,"style":821},[624],[569,1724,1726,1730,1733,1736,1804,1807,1810],{"className":1725},[611],[569,1727],{"className":1728,"style":1729},[615],"height:1.7936em;vertical-align:-0.686em;",[569,1731,590],{"className":1732},[620],[569,1734],{"className":1735,"style":625},[624],[569,1737,1739,1742,1801],{"className":1738},[629],[569,1740],{"className":1741},[1078,1079],[569,1743,1745],{"className":1744},[939],[569,1746,1748,1792],{"className":1747},[1031,1032],[569,1749,1751,1789],{"className":1750},[1036],[569,1752,1755,1767,1777],{"className":1753,"style":1754},[1040],"height:1.1076em;",[569,1756,1758,1761],{"style":1757},"top:-2.314em;",[569,1759],{"className":1760,"style":1049},[1048],[569,1762,1764],{"className":1763},[629],[569,1765,946],{"className":1766},[629],[569,1768,1770,1773],{"style":1769},"top:-3.23em;",[569,1771],{"className":1772,"style":1049},[1048],[569,1774],{"className":1775,"style":1776},[1120],"border-bottom-width:0.04em;",[569,1778,1780,1783],{"style":1779},"top:-3.677em;",[569,1781],{"className":1782,"style":1049},[1048],[569,1784,1786],{"className":1785},[629],[569,1787,943],{"className":1788,"style":1137},[629,630],[569,1790,1142],{"className":1791},[1141],[569,1793,1795],{"className":1794},[1036],[569,1796,1799],{"className":1797,"style":1798},[1040],"height:0.686em;",[569,1800],{},[569,1802],{"className":1803},[1155,1079],[569,1805],{"className":1806,"style":1368},[624],[569,1808,784],{"className":1809},[1372],[569,1811],{"className":1812,"style":1368},[624],[569,1814,1816,1819,1822,1825,1887,1890,1893],{"className":1815},[611],[569,1817],{"className":1818,"style":1729},[615],[569,1820,590],{"className":1821},[620],[569,1823],{"className":1824,"style":625},[624],[569,1826,1828,1831,1884],{"className":1827},[629],[569,1829],{"className":1830},[1078,1079],[569,1832,1834],{"className":1833},[939],[569,1835,1837,1876],{"className":1836},[1031,1032],[569,1838,1840,1873],{"className":1839},[1036],[569,1841,1843,1854,1862],{"className":1842,"style":1754},[1040],[569,1844,1845,1848],{"style":1757},[569,1846],{"className":1847,"style":1049},[1048],[569,1849,1851],{"className":1850},[629],[569,1852,1429],{"className":1853},[629],[569,1855,1856,1859],{"style":1769},[569,1857],{"className":1858,"style":1049},[1048],[569,1860],{"className":1861,"style":1776},[1120],[569,1863,1864,1867],{"style":1779},[569,1865],{"className":1866,"style":1049},[1048],[569,1868,1870],{"className":1869},[629],[569,1871,943],{"className":1872,"style":1137},[629,630],[569,1874,1142],{"className":1875},[1141],[569,1877,1879],{"className":1878},[1036],[569,1880,1882],{"className":1881,"style":1798},[1040],[569,1883],{},[569,1885],{"className":1886},[1155,1079],[569,1888],{"className":1889,"style":821},[624],[569,1891,964],{"className":1892},[825],[569,1894],{"className":1895,"style":821},[624],[569,1897,1899,1902,1905,1908,1911],{"className":1898},[611],[569,1900],{"className":1901,"style":1361},[615],[569,1903,993],{"className":1904},[629],[569,1906],{"className":1907,"style":1368},[624],[569,1909,784],{"className":1910},[1372],[569,1912],{"className":1913,"style":1368},[624],[569,1915,1917,1921,1984,1987,1990],{"className":1916},[611],[569,1918],{"className":1919,"style":1920},[615],"height:2.0074em;vertical-align:-0.686em;",[569,1922,1924,1927,1981],{"className":1923},[629],[569,1925],{"className":1926},[1078,1079],[569,1928,1930],{"className":1929},[939],[569,1931,1933,1973],{"className":1932},[1031,1032],[569,1934,1936,1970],{"className":1935},[1036],[569,1937,1940,1951,1959],{"className":1938,"style":1939},[1040],"height:1.3214em;",[569,1941,1942,1945],{"style":1757},[569,1943],{"className":1944,"style":1049},[1048],[569,1946,1948],{"className":1947},[629],[569,1949,946],{"className":1950},[629],[569,1952,1953,1956],{"style":1769},[569,1954],{"className":1955,"style":1049},[1048],[569,1957],{"className":1958,"style":1776},[1120],[569,1960,1961,1964],{"style":1779},[569,1962],{"className":1963,"style":1049},[1048],[569,1965,1967],{"className":1966},[629],[569,1968,993],{"className":1969},[629],[569,1971,1142],{"className":1972},[1141],[569,1974,1976],{"className":1975},[1036],[569,1977,1979],{"className":1978,"style":1798},[1040],[569,1980],{},[569,1982],{"className":1983},[1155,1079],[569,1985],{"className":1986,"style":821},[624],[569,1988,964],{"className":1989},[825],[569,1991],{"className":1992,"style":821},[624],[569,1994,1996,1999],{"className":1995},[611],[569,1997],{"className":1998,"style":1920},[615],[569,2000,2002,2005,2058],{"className":2001},[629],[569,2003],{"className":2004},[1078,1079],[569,2006,2008],{"className":2007},[939],[569,2009,2011,2050],{"className":2010},[1031,1032],[569,2012,2014,2047],{"className":2013},[1036],[569,2015,2017,2028,2036],{"className":2016,"style":1939},[1040],[569,2018,2019,2022],{"style":1757},[569,2020],{"className":2021,"style":1049},[1048],[569,2023,2025],{"className":2024},[629],[569,2026,946],{"className":2027},[629],[569,2029,2030,2033],{"style":1769},[569,2031],{"className":2032,"style":1049},[1048],[569,2034],{"className":2035,"style":1776},[1120],[569,2037,2038,2041],{"style":1779},[569,2039],{"className":2040,"style":1049},[1048],[569,2042,2044],{"className":2043},[629],[569,2045,993],{"className":2046},[629],[569,2048,1142],{"className":2049},[1141],[569,2051,2053],{"className":2052},[1036],[569,2054,2056],{"className":2055,"style":1798},[1040],[569,2057],{},[569,2059],{"className":2060},[1155,1079],[565,2062,2063,2064,2092,2093,2122],{},"Von ",[569,2065,2067,2080],{"className":2066},[572],[569,2068,2070],{"className":2069},[576],[578,2071,2072],{"xmlns":580},[582,2073,2074,2078],{},[585,2075,2076],{},[935,2077,937],{},[599,2079,937],{"encoding":601},[569,2081,2083],{"className":2082,"ariaHidden":607},[606],[569,2084,2086,2089],{"className":2085},[611],[569,2087],{"className":2088,"style":1382},[615],[569,2090,937],{"className":2091},[629]," bis ",[569,2094,2096,2110],{"className":2095},[572],[569,2097,2099],{"className":2098},[576],[578,2100,2101],{"xmlns":580},[582,2102,2103,2107],{},[585,2104,2105],{},[588,2106,943],{},[599,2108,2109],{"encoding":601},"\\pi",[569,2111,2113],{"className":2112,"ariaHidden":607},[606],[569,2114,2116,2119],{"className":2115},[611],[569,2117],{"className":2118,"style":663},[615],[569,2120,943],{"className":2121,"style":1137},[629,630]," heben sich die Teilflächen auf:",[569,2124,2126],{"className":2125},[914],[569,2127,2129,2181],{"className":2128},[572],[569,2130,2132],{"className":2131},[576],[578,2133,2134],{"xmlns":580,"display":923},[582,2135,2136,2178],{},[585,2137,2138,2146,2148,2150,2152,2154,2156,2158,2160,2162,2164,2166,2168,2170,2172,2174,2176],{},[929,2139,2140,2142,2144],{},[592,2141,933],{},[935,2143,937],{},[588,2145,943],{},[588,2147,646],{},[592,2149,594],{},[588,2151,597],{},[954,2153,956],{},[588,2155,959],{},[588,2157,597],{},[592,2159,964],{},[588,2161,590],{},[592,2163,594],{},[588,2165,943],{},[592,2167,784],{},[588,2169,590],{},[592,2171,594],{},[935,2173,937],{},[592,2175,964],{},[935,2177,937],{},[599,2179,2180],{"encoding":601},"\\int_0^{\\pi} \\cos x \\, dx = \\sin \\pi - \\sin 0 = 0",[569,2182,2184,2279,2303,2327],{"className":2183,"ariaHidden":607},[606],[569,2185,2187,2191,2249,2252,2255,2258,2261,2264,2267,2270,2273,2276],{"className":2186},[611],[569,2188],{"className":2189,"style":2190},[615],"height:2.3262em;vertical-align:-0.9119em;",[569,2192,2194,2197],{"className":2193},[620],[569,2195,933],{"className":2196,"style":1023},[620,1021,1022],[569,2198,2200],{"className":2199},[1027],[569,2201,2203,2241],{"className":2202},[1031,1032],[569,2204,2206,2238],{"className":2205},[1036],[569,2207,2210,2223],{"className":2208,"style":2209},[1040],"height:1.4143em;",[569,2211,2213,2217],{"style":2212},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[569,2214],{"className":2215,"style":2216},[1048],"height:2.7em;",[569,2218,2220],{"className":2219},[1053,1054,1055,1056],[569,2221,937],{"className":2222},[629,1056],[569,2224,2226,2229],{"style":2225},"top:-3.8129em;margin-right:0.05em;",[569,2227],{"className":2228,"style":2216},[1048],[569,2230,2232],{"className":2231},[1053,1054,1055,1056],[569,2233,2235],{"className":2234},[629,1056],[569,2236,943],{"className":2237,"style":1137},[629,630,1056],[569,2239,1142],{"className":2240},[1141],[569,2242,2244],{"className":2243},[1036],[569,2245,2247],{"className":2246,"style":1165},[1040],[569,2248],{},[569,2250],{"className":2251,"style":625},[624],[569,2253,646],{"className":2254},[620],[569,2256],{"className":2257,"style":625},[624],[569,2259,597],{"className":2260},[629,630],[569,2262],{"className":2263,"style":625},[624],[569,2265,959],{"className":2266},[629,630],[569,2268,597],{"className":2269},[629,630],[569,2271],{"className":2272,"style":821},[624],[569,2274,964],{"className":2275},[825],[569,2277],{"className":2278,"style":821},[624],[569,2280,2282,2285,2288,2291,2294,2297,2300],{"className":2281},[611],[569,2283],{"className":2284,"style":853},[615],[569,2286,590],{"className":2287},[620],[569,2289],{"className":2290,"style":625},[624],[569,2292,943],{"className":2293,"style":1137},[629,630],[569,2295],{"className":2296,"style":1368},[624],[569,2298,784],{"className":2299},[1372],[569,2301],{"className":2302,"style":1368},[624],[569,2304,2306,2309,2312,2315,2318,2321,2324],{"className":2305},[611],[569,2307],{"className":2308,"style":616},[615],[569,2310,590],{"className":2311},[620],[569,2313],{"className":2314,"style":625},[624],[569,2316,937],{"className":2317},[629],[569,2319],{"className":2320,"style":821},[624],[569,2322,964],{"className":2323},[825],[569,2325],{"className":2326,"style":821},[624],[569,2328,2330,2333],{"className":2329},[611],[569,2331],{"className":2332,"style":1382},[615],[569,2334,937],{"className":2335},[629],[565,2337,2338,2339,2436,2437,2540],{},"Die Fläche ist dort ",[569,2340,2342,2375],{"className":2341},[572],[569,2343,2345],{"className":2344},[576],[578,2346,2347],{"xmlns":580},[582,2348,2349,2372],{},[585,2350,2351,2353,2356,2360,2366,2368,2370],{},[935,2352,993],{},[592,2354,2355],{},"+",[588,2357,2359],{"mathvariant":2358},"normal","∣",[585,2361,2362,2364],{},[592,2363,784],{},[935,2365,993],{},[588,2367,2359],{"mathvariant":2358},[592,2369,964],{},[935,2371,946],{},[599,2373,2374],{"encoding":601},"1 + |{-1}| = 2",[569,2376,2378,2396,2427],{"className":2377,"ariaHidden":607},[606],[569,2379,2381,2384,2387,2390,2393],{"className":2380},[611],[569,2382],{"className":2383,"style":1361},[615],[569,2385,993],{"className":2386},[629],[569,2388],{"className":2389,"style":1368},[624],[569,2391,2355],{"className":2392},[1372],[569,2394],{"className":2395,"style":1368},[624],[569,2397,2399,2403,2406,2415,2418,2421,2424],{"className":2398},[611],[569,2400],{"className":2401,"style":2402},[615],"height:1em;vertical-align:-0.25em;",[569,2404,2359],{"className":2405},[629],[569,2407,2409,2412],{"className":2408},[629],[569,2410,784],{"className":2411},[629],[569,2413,993],{"className":2414},[629],[569,2416,2359],{"className":2417},[629],[569,2419],{"className":2420,"style":821},[624],[569,2422,964],{"className":2423},[825],[569,2425],{"className":2426,"style":821},[624],[569,2428,2430,2433],{"className":2429},[611],[569,2431],{"className":2432,"style":1382},[615],[569,2434,946],{"className":2435},[629],", weil man an der Nullstelle ",[569,2438,2440,2458],{"className":2439},[572],[569,2441,2443],{"className":2442},[576],[578,2444,2445],{"xmlns":580},[582,2446,2447,2455],{},[585,2448,2449],{},[939,2450,2451,2453],{},[588,2452,943],{},[935,2454,946],{},[599,2456,2457],{"encoding":601},"\\frac{\\pi}{2}",[569,2459,2461],{"className":2460,"ariaHidden":607},[606],[569,2462,2464,2468],{"className":2463},[611],[569,2465],{"className":2466,"style":2467},[615],"height:1.0404em;vertical-align:-0.345em;",[569,2469,2471,2474,2537],{"className":2470},[629],[569,2472],{"className":2473},[1078,1079],[569,2475,2477],{"className":2476},[939],[569,2478,2480,2528],{"className":2479},[1031,1032],[569,2481,2483,2525],{"className":2482},[1036],[569,2484,2487,2502,2510],{"className":2485,"style":2486},[1040],"height:0.6954em;",[569,2488,2490,2493],{"style":2489},"top:-2.655em;",[569,2491],{"className":2492,"style":1049},[1048],[569,2494,2496],{"className":2495},[1053,1054,1055,1056],[569,2497,2499],{"className":2498},[629,1056],[569,2500,946],{"className":2501},[629,1056],[569,2503,2504,2507],{"style":1769},[569,2505],{"className":2506,"style":1049},[1048],[569,2508],{"className":2509,"style":1776},[1120],[569,2511,2513,2516],{"style":2512},"top:-3.394em;",[569,2514],{"className":2515,"style":1049},[1048],[569,2517,2519],{"className":2518},[1053,1054,1055,1056],[569,2520,2522],{"className":2521},[629,1056],[569,2523,943],{"className":2524,"style":1137},[629,630,1056],[569,2526,1142],{"className":2527},[1141],[569,2529,2531],{"className":2530},[1036],[569,2532,2535],{"className":2533,"style":2534},[1040],"height:0.345em;",[569,2536],{},[569,2538],{"className":2539},[1155,1079]," aufteilen muss.",[560,2542,2544],{"id":2543},"typische-fehler","Typische Fehler",[2546,2547,2548,2661,2789],"ul",{},[2549,2550,2551,2552,631,2657,2660],"li",{},"Ein Minuszeichen ergänzen: ",[569,2553,2555,2591],{"className":2554},[572],[569,2556,2558],{"className":2557},[576],[578,2559,2560],{"xmlns":580},[582,2561,2562,2588],{},[585,2563,2564,2566,2568,2570,2572,2574,2576,2578,2580,2582,2584,2586],{},[592,2565,933],{},[588,2567,646],{},[592,2569,594],{},[588,2571,597],{},[954,2573,956],{},[588,2575,959],{},[588,2577,597],{},[592,2579,964],{},[592,2581,784],{},[588,2583,590],{},[592,2585,594],{},[588,2587,597],{},[599,2589,2590],{"encoding":601},"\\int \\cos x\\,dx = -\\sin x",[569,2592,2594,2636],{"className":2593,"ariaHidden":607},[606],[569,2595,2597,2601,2606,2609,2612,2615,2618,2621,2624,2627,2630,2633],{"className":2596},[611],[569,2598],{"className":2599,"style":2600},[615],"height:1.1111em;vertical-align:-0.3061em;",[569,2602,933],{"className":2603,"style":2605},[620,1021,2604],"small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[569,2607],{"className":2608,"style":625},[624],[569,2610,646],{"className":2611},[620],[569,2613],{"className":2614,"style":625},[624],[569,2616,597],{"className":2617},[629,630],[569,2619],{"className":2620,"style":625},[624],[569,2622,959],{"className":2623},[629,630],[569,2625,597],{"className":2626},[629,630],[569,2628],{"className":2629,"style":821},[624],[569,2631,964],{"className":2632},[825],[569,2634],{"className":2635,"style":821},[624],[569,2637,2639,2642,2645,2648,2651,2654],{"className":2638},[611],[569,2640],{"className":2641,"style":853},[615],[569,2643,784],{"className":2644},[629],[569,2646],{"className":2647,"style":625},[624],[569,2649,590],{"className":2650},[620],[569,2652],{"className":2653,"style":625},[624],[569,2655,597],{"className":2656},[629,630],[714,2658,2659],{},"falsch",". Das Minus gehört zum Integral des Sinus.",[2549,2662,2663,2664,631,2702,2749,2750,2788],{},"Ableitung und Stammfunktion verwechseln: Die Ableitung von ",[569,2665,2667,2684],{"className":2666},[572],[569,2668,2670],{"className":2669},[576],[578,2671,2672],{"xmlns":580},[582,2673,2674,2682],{},[585,2675,2676,2678,2680],{},[588,2677,646],{},[592,2679,594],{},[588,2681,597],{},[599,2683,653],{"encoding":601},[569,2685,2687],{"className":2686,"ariaHidden":607},[606],[569,2688,2690,2693,2696,2699],{"className":2689},[611],[569,2691],{"className":2692,"style":663},[615],[569,2694,646],{"className":2695},[620],[569,2697],{"className":2698,"style":625},[624],[569,2700,597],{"className":2701},[629,630],[569,2703,2705,2725],{"className":2704},[572],[569,2706,2708],{"className":2707},[576],[578,2709,2710],{"xmlns":580},[582,2711,2712,2722],{},[585,2713,2714,2716,2718,2720],{},[592,2715,784],{},[588,2717,590],{},[592,2719,594],{},[588,2721,597],{},[599,2723,2724],{"encoding":601},"-\\sin x",[569,2726,2728],{"className":2727,"ariaHidden":607},[606],[569,2729,2731,2734,2737,2740,2743,2746],{"className":2730},[611],[569,2732],{"className":2733,"style":853},[615],[569,2735,784],{"className":2736},[629],[569,2738],{"className":2739,"style":625},[624],[569,2741,590],{"className":2742},[620],[569,2744],{"className":2745,"style":625},[624],[569,2747,597],{"className":2748},[629,630],", die Stammfunktion ist ",[569,2751,2753,2770],{"className":2752},[572],[569,2754,2756],{"className":2755},[576],[578,2757,2758],{"xmlns":580},[582,2759,2760,2768],{},[585,2761,2762,2764,2766],{},[588,2763,590],{},[592,2765,594],{},[588,2767,597],{},[599,2769,602],{"encoding":601},[569,2771,2773],{"className":2772,"ariaHidden":607},[606],[569,2774,2776,2779,2782,2785],{"className":2775},[611],[569,2777],{"className":2778,"style":616},[615],[569,2780,590],{"className":2781},[620],[569,2783],{"className":2784,"style":625},[624],[569,2786,597],{"className":2787},[629,630],".",[2549,2790,2791,2792,2847,2848,2948,2949,2788],{},"Bei ",[569,2793,2795,2823],{"className":2794},[572],[569,2796,2798],{"className":2797},[576],[578,2799,2800],{"xmlns":580},[582,2801,2802,2820],{},[585,2803,2804,2806,2808,2812,2815,2817],{},[588,2805,646],{},[592,2807,594],{},[592,2809,2811],{"stretchy":2810},"false","(",[935,2813,2814],{},"3",[588,2816,597],{},[592,2818,2819],{"stretchy":2810},")",[599,2821,2822],{"encoding":601},"\\cos(3x)",[569,2824,2826],{"className":2825,"ariaHidden":607},[606],[569,2827,2829,2832,2835,2838,2841,2844],{"className":2828},[611],[569,2830],{"className":2831,"style":2402},[615],[569,2833,646],{"className":2834},[620],[569,2836,2811],{"className":2837},[1078],[569,2839,2814],{"className":2840},[629],[569,2842,597],{"className":2843},[629,630],[569,2845,2819],{"className":2846},[1155]," den Faktor ",[569,2849,2851,2869],{"className":2850},[572],[569,2852,2854],{"className":2853},[576],[578,2855,2856],{"xmlns":580},[582,2857,2858,2866],{},[585,2859,2860],{},[939,2861,2862,2864],{},[935,2863,993],{},[935,2865,2814],{},[599,2867,2868],{"encoding":601},"\\frac{1}{3}",[569,2870,2872],{"className":2871,"ariaHidden":607},[606],[569,2873,2875,2879],{"className":2874},[611],[569,2876],{"className":2877,"style":2878},[615],"height:1.1901em;vertical-align:-0.345em;",[569,2880,2882,2885,2945],{"className":2881},[629],[569,2883],{"className":2884},[1078,1079],[569,2886,2888],{"className":2887},[939],[569,2889,2891,2937],{"className":2890},[1031,1032],[569,2892,2894,2934],{"className":2893},[1036],[569,2895,2898,2912,2920],{"className":2896,"style":2897},[1040],"height:0.8451em;",[569,2899,2900,2903],{"style":2489},[569,2901],{"className":2902,"style":1049},[1048],[569,2904,2906],{"className":2905},[1053,1054,1055,1056],[569,2907,2909],{"className":2908},[629,1056],[569,2910,2814],{"className":2911},[629,1056],[569,2913,2914,2917],{"style":1769},[569,2915],{"className":2916,"style":1049},[1048],[569,2918],{"className":2919,"style":1776},[1120],[569,2921,2922,2925],{"style":2512},[569,2923],{"className":2924,"style":1049},[1048],[569,2926,2928],{"className":2927},[1053,1054,1055,1056],[569,2929,2931],{"className":2930},[629,1056],[569,2932,993],{"className":2933},[629,1056],[569,2935,1142],{"className":2936},[1141],[569,2938,2940],{"className":2939},[1036],[569,2941,2943],{"className":2942,"style":2534},[1040],[569,2944],{},[569,2946],{"className":2947},[1155,1079]," vergessen: ",[569,2950,2952,3009],{"className":2951},[572],[569,2953,2955],{"className":2954},[576],[578,2956,2957],{"xmlns":580},[582,2958,2959,3006],{},[585,2960,2961,2963,2965,2967,2969,2971,2973,2975,2977,2979,2981,2983,2989,2991,2993,2995,2997,2999,3001,3003],{},[592,2962,933],{},[588,2964,646],{},[592,2966,594],{},[592,2968,2811],{"stretchy":2810},[935,2970,2814],{},[588,2972,597],{},[592,2974,2819],{"stretchy":2810},[954,2976,956],{},[588,2978,959],{},[588,2980,597],{},[592,2982,964],{},[939,2984,2985,2987],{},[935,2986,993],{},[935,2988,2814],{},[588,2990,590],{},[592,2992,594],{},[592,2994,2811],{"stretchy":2810},[935,2996,2814],{},[588,2998,597],{},[592,3000,2819],{"stretchy":2810},[592,3002,2355],{},[588,3004,3005],{},"C",[599,3007,3008],{"encoding":601},"\\int \\cos(3x)\\,dx = \\frac{1}{3}\\sin(3x) + C",[569,3010,3012,3057,3158],{"className":3011,"ariaHidden":607},[606],[569,3013,3015,3018,3021,3024,3027,3030,3033,3036,3039,3042,3045,3048,3051,3054],{"className":3014},[611],[569,3016],{"className":3017,"style":2600},[615],[569,3019,933],{"className":3020,"style":2605},[620,1021,2604],[569,3022],{"className":3023,"style":625},[624],[569,3025,646],{"className":3026},[620],[569,3028,2811],{"className":3029},[1078],[569,3031,2814],{"className":3032},[629],[569,3034,597],{"className":3035},[629,630],[569,3037,2819],{"className":3038},[1155],[569,3040],{"className":3041,"style":625},[624],[569,3043,959],{"className":3044},[629,630],[569,3046,597],{"className":3047},[629,630],[569,3049],{"className":3050,"style":821},[624],[569,3052,964],{"className":3053},[825],[569,3055],{"className":3056,"style":821},[624],[569,3058,3060,3063,3131,3134,3137,3140,3143,3146,3149,3152,3155],{"className":3059},[611],[569,3061],{"className":3062,"style":2878},[615],[569,3064,3066,3069,3128],{"className":3065},[629],[569,3067],{"className":3068},[1078,1079],[569,3070,3072],{"className":3071},[939],[569,3073,3075,3120],{"className":3074},[1031,1032],[569,3076,3078,3117],{"className":3077},[1036],[569,3079,3081,3095,3103],{"className":3080,"style":2897},[1040],[569,3082,3083,3086],{"style":2489},[569,3084],{"className":3085,"style":1049},[1048],[569,3087,3089],{"className":3088},[1053,1054,1055,1056],[569,3090,3092],{"className":3091},[629,1056],[569,3093,2814],{"className":3094},[629,1056],[569,3096,3097,3100],{"style":1769},[569,3098],{"className":3099,"style":1049},[1048],[569,3101],{"className":3102,"style":1776},[1120],[569,3104,3105,3108],{"style":2512},[569,3106],{"className":3107,"style":1049},[1048],[569,3109,3111],{"className":3110},[1053,1054,1055,1056],[569,3112,3114],{"className":3113},[629,1056],[569,3115,993],{"className":3116},[629,1056],[569,3118,1142],{"className":3119},[1141],[569,3121,3123],{"className":3122},[1036],[569,3124,3126],{"className":3125,"style":2534},[1040],[569,3127],{},[569,3129],{"className":3130},[1155,1079],[569,3132],{"className":3133,"style":625},[624],[569,3135,590],{"className":3136},[620],[569,3138,2811],{"className":3139},[1078],[569,3141,2814],{"className":3142},[629],[569,3144,597],{"className":3145},[629,630],[569,3147,2819],{"className":3148},[1155],[569,3150],{"className":3151,"style":1368},[624],[569,3153,2355],{"className":3154},[1372],[569,3156],{"className":3157,"style":1368},[624],[569,3159,3161,3165],{"className":3160},[611],[569,3162],{"className":3163,"style":3164},[615],"height:0.6833em;",[569,3166,3005],{"className":3167,"style":3168},[629,630],"margin-right:0.0715em;",{"title":3170,"searchDepth":3171,"depth":3171,"links":3172},"",2,[3173,3174,3175],{"id":562,"depth":3171,"text":563},{"id":909,"depth":3171,"text":910},{"id":2543,"depth":3171,"text":2544},[3177,3179,3181,3184,3186],{"lhs":3178,"rhs":993},"round(sum(map(0:999, f(k) = cos((k + 0.5) * pi \u002F 2000))) * pi \u002F 2000, 4)",{"lhs":3180,"rhs":993},"sin(pi\u002F2) - sin(0)",{"lhs":3182,"rhs":3183},"sin(pi\u002F2) - sin(pi\u002F6)","1\u002F2",{"lhs":3185,"rhs":937},"sin(pi) - sin(0)",{"lhs":3187,"rhs":946},"(sin(pi\u002F2) - sin(0)) + abs(sin(pi) - sin(pi\u002F2))","x \\text{ im Bogenmaß}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x\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\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">im Bogenmaß\u003C\u002Fspan>",null,"md","integral-cosine","\\int \\cos x \\, dx = \\sin x + C","\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>\u003Cmo>∫\u003C\u002Fmo>\u003Cmi>cos\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\int \\cos x \\, dx = \\sin x + 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:2.2222em;vertical-align:-0.8622em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">cos\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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:0.7512em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegral-kosinus",[],[3201,3202,3203,3204],"integral-sine","fundamental-theorem","degrees-radians","linear-substitution",{"title":548,"description":3170},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegral-kosinus","Eine Stammfunktion des Kosinus ist der Sinus.",[3209,3210,3211,3212],"kosinus","stammfunktion","integral","trigonometrie",[3214,3217],{"symbol":597,"meaning":3215,"symbolHtml":3216},"Integrationsvariable, Winkel im Bogenmaß","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x\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\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3005,"meaning":3218,"symbolHtml":3219},"Integrationskonstante","\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","A5haqusQC9DG5yGFXTYCKSuFnT6F2KTEOswlUsOxFL4",[3222,3225,3228,3231],{"stem":3223,"title":3224,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fhauptsatz-der-differential-und-integralrechnung","Hauptsatz der Differential- und Integralrechnung",{"stem":3226,"title":3227,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fintegral-sinus","Integral des Sinus",{"stem":3229,"title":3230,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Flineare-substitution","Lineare Substitution",{"stem":3232,"title":3233,"category":518},"de\u002Fformulas\u002Fmath\u002Ftrigonometry\u002Fumrechnung-gradmass-bogenmass","Umrechnung Gradmaß in Bogenmaß",1793824282040]