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Nach dem Hauptsatz ist jede Integralfunktion einer stetigen Funktion eine ",[569,1070,1071],{},"Stammfunktion"," von ",[573,1074,1076,1089],{"className":1075},[576],[573,1077,1079],{"className":1078},[580],[582,1080,1081],{"xmlns":584},[586,1082,1083,1087],{},[589,1084,1085],{},[592,1086,953],{},[596,1088,953],{"encoding":598},[573,1090,1092],{"className":1091,"ariaHidden":603},[602],[573,1093,1095,1099],{"className":1094},[607],[573,1096],{"className":1097,"style":1098},[611],"height:0.8889em;vertical-align:-0.1944em;",[573,1100,953],{"className":1101,"style":1058},[616,617],".",[774,1104,1105,1106,1134,1135,1163,1164,1102],{},"Liegt ",[573,1107,1109,1122],{"className":1108},[576],[573,1110,1112],{"className":1111},[580],[582,1113,1114],{"xmlns":584},[586,1115,1116,1120],{},[589,1117,1118],{},[592,1119,633],{},[596,1121,633],{"encoding":598},[573,1123,1125],{"className":1124,"ariaHidden":603},[602],[573,1126,1128,1131],{"className":1127},[607],[573,1129],{"className":1130,"style":612},[611],[573,1132,633],{"className":1133},[616,617]," links von ",[573,1136,1138,1151],{"className":1137},[576],[573,1139,1141],{"className":1140},[580],[582,1142,1143],{"xmlns":584},[586,1144,1145,1149],{},[589,1146,1147],{},[592,1148,594],{},[596,1150,594],{"encoding":598},[573,1152,1154],{"className":1153,"ariaHidden":603},[602],[573,1155,1157,1160],{"className":1156},[607],[573,1158],{"className":1159,"style":612},[611],[573,1161,594],{"className":1162},[616,617],", ist ",[573,1165,1167,1222],{"className":1166},[576],[573,1168,1170],{"className":1169},[580],[582,1171,1172],{"xmlns":584},[586,1173,1174,1219],{},[589,1175,1176,1182,1184,1186,1188,1190,1193,1202,1204,1206,1208,1210,1214,1217],{},[789,1177,1178,1180],{},[592,1179,793],{},[592,1181,594],{},[797,1183,800],{"stretchy":799},[592,1185,633],{},[797,1187,805],{"stretchy":799},[797,1189,808],{},[797,1191,1192],{},"−",[932,1194,1195,1198,1200],{},[797,1196,1197],{},"∫",[592,1199,633],{},[592,1201,594],{},[592,1203,953],{},[797,1205,800],{"stretchy":799},[592,1207,721],{},[797,1209,805],{"stretchy":799},[1211,1212,1213],"mtext",{}," ",[592,1215,1216],{},"d",[592,1218,721],{},[596,1220,1221],{"encoding":598},"I_a(x) = -\\int_x^a f(t)\\,dt",[573,1223,1225,1289],{"className":1224,"ariaHidden":603},[602],[573,1226,1228,1231,1271,1274,1277,1280,1283,1286],{"className":1227},[607],[573,1229],{"className":1230,"style":825},[611],[573,1232,1234,1237],{"className":1233},[616],[573,1235,793],{"className":1236,"style":832},[616,617],[573,1238,1240],{"className":1239},[836],[573,1241,1243,1263],{"className":1242},[840,841],[573,1244,1246,1260],{"className":1245},[845],[573,1247,1249],{"className":1248,"style":850},[849],[573,1250,1251,1254],{"style":853},[573,1252],{"className":1253,"style":858},[857],[573,1255,1257],{"className":1256},[862,863,864,865],[573,1258,594],{"className":1259},[616,617,865],[573,1261,873],{"className":1262},[872],[573,1264,1266],{"className":1265},[845],[573,1267,1269],{"className":1268,"style":880},[849],[573,1270],{},[573,1272,800],{"className":1273},[886],[573,1275,633],{"className":1276},[616,617],[573,1278,805],{"className":1279},[893],[573,1281],{"className":1282,"style":898},[897],[573,1284,808],{"className":1285},[902],[573,1287],{"className":1288,"style":898},[897],[573,1290,1292,1296,1299,1303,1362,1365,1368,1371,1374,1377,1380,1383],{"className":1291},[607],[573,1293],{"className":1294,"style":1295},[611],"height:1.2151em;vertical-align:-0.3558em;",[573,1297,1192],{"className":1298},[616],[573,1300],{"className":1301,"style":1302},[897],"margin-right:0.1667em;",[573,1304,1307,1313],{"className":1305},[1306],"mop",[573,1308,1197],{"className":1309,"style":1312},[1306,1310,1311],"op-symbol","small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[573,1314,1316],{"className":1315},[836],[573,1317,1319,1353],{"className":1318},[840,841],[573,1320,1322,1350],{"className":1321},[845],[573,1323,1326,1338],{"className":1324,"style":1325},[849],"height:0.8593em;",[573,1327,1329,1332],{"style":1328},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[573,1330],{"className":1331,"style":858},[857],[573,1333,1335],{"className":1334},[862,863,864,865],[573,1336,633],{"className":1337},[616,617,865],[573,1339,1341,1344],{"style":1340},"top:-3.2579em;margin-right:0.05em;",[573,1342],{"className":1343,"style":858},[857],[573,1345,1347],{"className":1346},[862,863,864,865],[573,1348,594],{"className":1349},[616,617,865],[573,1351,873],{"className":1352},[872],[573,1354,1356],{"className":1355},[845],[573,1357,1360],{"className":1358,"style":1359},[849],"height:0.3558em;",[573,1361],{},[573,1363],{"className":1364,"style":1302},[897],[573,1366,953],{"className":1367,"style":1058},[616,617],[573,1369,800],{"className":1370},[886],[573,1372,721],{"className":1373},[616,617],[573,1375,805],{"className":1376},[893],[573,1378],{"className":1379,"style":1302},[897],[573,1381,1216],{"className":1382},[616,617],[573,1384,721],{"className":1385},[616,617],[774,1387,1388],{},"Zwei Integralfunktionen zu verschiedenen unteren Grenzen unterscheiden sich nur um eine Konstante.",[565,1390,1391,1392,1481,1482,1553,1554,1625],{},"Die Umkehrung gilt nicht: Nicht jede Stammfunktion ist eine Integralfunktion. Eine Stammfunktion ohne Nullstelle, wie ",[573,1393,1395,1421],{"className":1394},[576],[573,1396,1398],{"className":1397},[580],[582,1399,1400],{"xmlns":584},[586,1401,1402,1418],{},[589,1403,1404,1412,1415],{},[1405,1406,1407,1409],"msup",{},[592,1408,633],{},[810,1410,1411],{},"2",[797,1413,1414],{},"+",[810,1416,1417],{},"1",[596,1419,1420],{"encoding":598},"x^2 + 1",[573,1422,1424,1472],{"className":1423,"ariaHidden":603},[602],[573,1425,1427,1431,1461,1465,1469],{"className":1426},[607],[573,1428],{"className":1429,"style":1430},[611],"height:0.8974em;vertical-align:-0.0833em;",[573,1432,1434,1437],{"className":1433},[616],[573,1435,633],{"className":1436},[616,617],[573,1438,1440],{"className":1439},[836],[573,1441,1443],{"className":1442},[840],[573,1444,1446],{"className":1445},[845],[573,1447,1450],{"className":1448,"style":1449},[849],"height:0.8141em;",[573,1451,1452,1455],{"style":1006},[573,1453],{"className":1454,"style":858},[857],[573,1456,1458],{"className":1457},[862,863,864,865],[573,1459,1411],{"className":1460},[616,865],[573,1462],{"className":1463,"style":1464},[897],"margin-right:0.2222em;",[573,1466,1414],{"className":1467},[1468],"mbin",[573,1470],{"className":1471,"style":1464},[897],[573,1473,1475,1478],{"className":1474},[607],[573,1476],{"className":1477,"style":912},[611],[573,1479,1417],{"className":1480},[616]," zu ",[573,1483,1485,1511],{"className":1484},[576],[573,1486,1488],{"className":1487},[580],[582,1489,1490],{"xmlns":584},[586,1491,1492,1508],{},[589,1493,1494,1496,1498,1500,1502,1504,1506],{},[592,1495,953],{},[797,1497,800],{"stretchy":799},[592,1499,633],{},[797,1501,805],{"stretchy":799},[797,1503,808],{},[810,1505,1411],{},[592,1507,633],{},[596,1509,1510],{"encoding":598},"f(x) = 2x",[573,1512,1514,1541],{"className":1513,"ariaHidden":603},[602],[573,1515,1517,1520,1523,1526,1529,1532,1535,1538],{"className":1516},[607],[573,1518],{"className":1519,"style":825},[611],[573,1521,953],{"className":1522,"style":1058},[616,617],[573,1524,800],{"className":1525},[886],[573,1527,633],{"className":1528},[616,617],[573,1530,805],{"className":1531},[893],[573,1533],{"className":1534,"style":898},[897],[573,1536,808],{"className":1537},[902],[573,1539],{"className":1540,"style":898},[897],[573,1542,1544,1547,1550],{"className":1543},[607],[573,1545],{"className":1546,"style":912},[611],[573,1548,1411],{"className":1549},[616],[573,1551,633],{"className":1552},[616,617],", lässt sich nicht als ",[573,1555,1557,1575],{"className":1556},[576],[573,1558,1560],{"className":1559},[580],[582,1561,1562],{"xmlns":584},[586,1563,1564,1572],{},[589,1565,1566],{},[789,1567,1568,1570],{},[592,1569,793],{},[592,1571,594],{},[596,1573,1574],{"encoding":598},"I_a",[573,1576,1578],{"className":1577,"ariaHidden":603},[602],[573,1579,1581,1585],{"className":1580},[607],[573,1582],{"className":1583,"style":1584},[611],"height:0.8333em;vertical-align:-0.15em;",[573,1586,1588,1591],{"className":1587},[616],[573,1589,793],{"className":1590,"style":832},[616,617],[573,1592,1594],{"className":1593},[836],[573,1595,1597,1617],{"className":1596},[840,841],[573,1598,1600,1614],{"className":1599},[845],[573,1601,1603],{"className":1602,"style":850},[849],[573,1604,1605,1608],{"style":853},[573,1606],{"className":1607,"style":858},[857],[573,1609,1611],{"className":1610},[862,863,864,865],[573,1612,594],{"className":1613},[616,617,865],[573,1615,873],{"className":1616},[872],[573,1618,1620],{"className":1619},[845],[573,1621,1623],{"className":1622,"style":880},[849],[573,1624],{}," schreiben.",[560,1627,1629],{"id":1628},"beispiele","Beispiele",[565,1631,1632,1633,1704,1705,1756],{},"Für ",[573,1634,1636,1662],{"className":1635},[576],[573,1637,1639],{"className":1638},[580],[582,1640,1641],{"xmlns":584},[586,1642,1643,1659],{},[589,1644,1645,1647,1649,1651,1653,1655,1657],{},[592,1646,953],{},[797,1648,800],{"stretchy":799},[592,1650,721],{},[797,1652,805],{"stretchy":799},[797,1654,808],{},[810,1656,1411],{},[592,1658,721],{},[596,1660,1661],{"encoding":598},"f(t) = 2t",[573,1663,1665,1692],{"className":1664,"ariaHidden":603},[602],[573,1666,1668,1671,1674,1677,1680,1683,1686,1689],{"className":1667},[607],[573,1669],{"className":1670,"style":825},[611],[573,1672,953],{"className":1673,"style":1058},[616,617],[573,1675,800],{"className":1676},[886],[573,1678,721],{"className":1679},[616,617],[573,1681,805],{"className":1682},[893],[573,1684],{"className":1685,"style":898},[897],[573,1687,808],{"className":1688},[902],[573,1690],{"className":1691,"style":898},[897],[573,1693,1695,1698,1701],{"className":1694},[607],[573,1696],{"className":1697,"style":912},[611],[573,1699,1411],{"className":1700},[616],[573,1702,721],{"className":1703},[616,617]," und die untere Grenze ",[573,1706,1708,1726],{"className":1707},[576],[573,1709,1711],{"className":1710},[580],[582,1712,1713],{"xmlns":584},[586,1714,1715,1723],{},[589,1716,1717,1719,1721],{},[592,1718,594],{},[797,1720,808],{},[810,1722,1417],{},[596,1724,1725],{"encoding":598},"a = 1",[573,1727,1729,1747],{"className":1728,"ariaHidden":603},[602],[573,1730,1732,1735,1738,1741,1744],{"className":1731},[607],[573,1733],{"className":1734,"style":612},[611],[573,1736,594],{"className":1737},[616,617],[573,1739],{"className":1740,"style":898},[897],[573,1742,808],{"className":1743},[902],[573,1745],{"className":1746,"style":898},[897],[573,1748,1750,1753],{"className":1749},[607],[573,1751],{"className":1752,"style":912},[611],[573,1754,1417],{"className":1755},[616],":",[573,1758,1761],{"className":1759},[1760],"katex-display",[573,1762,1764,1842],{"className":1763},[576],[573,1765,1767],{"className":1766},[580],[582,1768,1770],{"xmlns":584,"display":1769},"block",[586,1771,1772,1839],{},[589,1773,1774,1780,1782,1784,1786,1788,1796,1798,1800,1802,1804,1806,1808,1812,1818,1827,1829,1835,1837],{},[789,1775,1776,1778],{},[592,1777,793],{},[810,1779,1417],{},[797,1781,800],{"stretchy":799},[592,1783,633],{},[797,1785,805],{"stretchy":799},[797,1787,808],{},[932,1789,1790,1792,1794],{},[797,1791,1197],{},[810,1793,1417],{},[592,1795,633],{},[810,1797,1411],{},[592,1799,721],{},[1211,1801,1213],{},[592,1803,1216],{},[592,1805,721],{},[797,1807,808],{},[797,1809,1811],{"fence":799,"stretchy":603,"minsize":1810,"maxsize":1810},"1.8em","[",[1405,1813,1814,1816],{},[592,1815,721],{},[810,1817,1411],{},[932,1819,1820,1823,1825],{},[797,1821,1822],{"fence":799,"stretchy":603,"minsize":1810,"maxsize":1810},"]",[810,1824,1417],{},[592,1826,633],{},[797,1828,808],{},[1405,1830,1831,1833],{},[592,1832,633],{},[810,1834,1411],{},[797,1836,1192],{},[810,1838,1417],{},[596,1840,1841],{"encoding":598},"I_1(x) = \\int_1^x 2t\\,dt = \\Big[t^2\\Big]_1^x = x^2 - 1",[573,1843,1845,1910,2001,2114,2159],{"className":1844,"ariaHidden":603},[602],[573,1846,1848,1851,1892,1895,1898,1901,1904,1907],{"className":1847},[607],[573,1849],{"className":1850,"style":825},[611],[573,1852,1854,1857],{"className":1853},[616],[573,1855,793],{"className":1856,"style":832},[616,617],[573,1858,1860],{"className":1859},[836],[573,1861,1863,1884],{"className":1862},[840,841],[573,1864,1866,1881],{"className":1865},[845],[573,1867,1870],{"className":1868,"style":1869},[849],"height:0.3011em;",[573,1871,1872,1875],{"style":853},[573,1873],{"className":1874,"style":858},[857],[573,1876,1878],{"className":1877},[862,863,864,865],[573,1879,1417],{"className":1880},[616,865],[573,1882,873],{"className":1883},[872],[573,1885,1887],{"className":1886},[845],[573,1888,1890],{"className":1889,"style":880},[849],[573,1891],{},[573,1893,800],{"className":1894},[886],[573,1896,633],{"className":1897},[616,617],[573,1899,805],{"className":1900},[893],[573,1902],{"className":1903,"style":898},[897],[573,1905,808],{"className":1906},[902],[573,1908],{"className":1909,"style":898},[897],[573,1911,1913,1917,1974,1977,1980,1983,1986,1989,1992,1995,1998],{"className":1912},[607],[573,1914],{"className":1915,"style":1916},[611],"height:2.3262em;vertical-align:-0.9119em;",[573,1918,1920,1925],{"className":1919},[1306],[573,1921,1197],{"className":1922,"style":1924},[1306,1310,1923],"large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[573,1926,1928],{"className":1927},[836],[573,1929,1931,1965],{"className":1930},[840,841],[573,1932,1934,1962],{"className":1933},[845],[573,1935,1938,1950],{"className":1936,"style":1937},[849],"height:1.4143em;",[573,1939,1941,1944],{"style":1940},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[573,1942],{"className":1943,"style":858},[857],[573,1945,1947],{"className":1946},[862,863,864,865],[573,1948,1417],{"className":1949},[616,865],[573,1951,1953,1956],{"style":1952},"top:-3.8129em;margin-right:0.05em;",[573,1954],{"className":1955,"style":858},[857],[573,1957,1959],{"className":1958},[862,863,864,865],[573,1960,633],{"className":1961},[616,617,865],[573,1963,873],{"className":1964},[872],[573,1966,1968],{"className":1967},[845],[573,1969,1972],{"className":1970,"style":1971},[849],"height:0.9119em;",[573,1973],{},[573,1975],{"className":1976,"style":1302},[897],[573,1978,1411],{"className":1979},[616],[573,1981,721],{"className":1982},[616,617],[573,1984],{"className":1985,"style":1302},[897],[573,1987,1216],{"className":1988},[616,617],[573,1990,721],{"className":1991},[616,617],[573,1993],{"className":1994,"style":898},[897],[573,1996,808],{"className":1997},[902],[573,1999],{"className":2000,"style":898},[897],[573,2002,2004,2008,2016,2047,2105,2108,2111],{"className":2003},[607],[573,2005],{"className":2006,"style":2007},[611],"height:1.904em;vertical-align:-0.6997em;",[573,2009,2011],{"className":2010},[616],[573,2012,1811],{"className":2013},[2014,2015],"delimsizing","size2",[573,2017,2019,2022],{"className":2018},[616],[573,2020,721],{"className":2021},[616,617],[573,2023,2025],{"className":2024},[836],[573,2026,2028],{"className":2027},[840],[573,2029,2031],{"className":2030},[845],[573,2032,2035],{"className":2033,"style":2034},[849],"height:0.8641em;",[573,2036,2038,2041],{"style":2037},"top:-3.113em;margin-right:0.05em;",[573,2039],{"className":2040,"style":858},[857],[573,2042,2044],{"className":2043},[862,863,864,865],[573,2045,1411],{"className":2046},[616,865],[573,2048,2050,2056],{"className":2049},[616],[573,2051,2053],{"className":2052},[616],[573,2054,1822],{"className":2055},[2014,2015],[573,2057,2059],{"className":2058},[836],[573,2060,2062,2096],{"className":2061},[840,841],[573,2063,2065,2093],{"className":2064},[845],[573,2066,2069,2081],{"className":2067,"style":2068},[849],"height:1.2043em;",[573,2070,2072,2075],{"style":2071},"top:-2.0003em;margin-right:0.05em;",[573,2073],{"className":2074,"style":858},[857],[573,2076,2078],{"className":2077},[862,863,864,865],[573,2079,1417],{"className":2080},[616,865],[573,2082,2084,2087],{"style":2083},"top:-3.6029em;margin-right:0.05em;",[573,2085],{"className":2086,"style":858},[857],[573,2088,2090],{"className":2089},[862,863,864,865],[573,2091,633],{"className":2092},[616,617,865],[573,2094,873],{"className":2095},[872],[573,2097,2099],{"className":2098},[845],[573,2100,2103],{"className":2101,"style":2102},[849],"height:0.6997em;",[573,2104],{},[573,2106],{"className":2107,"style":898},[897],[573,2109,808],{"className":2110},[902],[573,2112],{"className":2113,"style":898},[897],[573,2115,2117,2121,2150,2153,2156],{"className":2116},[607],[573,2118],{"className":2119,"style":2120},[611],"height:0.9474em;vertical-align:-0.0833em;",[573,2122,2124,2127],{"className":2123},[616],[573,2125,633],{"className":2126},[616,617],[573,2128,2130],{"className":2129},[836],[573,2131,2133],{"className":2132},[840],[573,2134,2136],{"className":2135},[845],[573,2137,2139],{"className":2138,"style":2034},[849],[573,2140,2141,2144],{"style":2037},[573,2142],{"className":2143,"style":858},[857],[573,2145,2147],{"className":2146},[862,863,864,865],[573,2148,1411],{"className":2149},[616,865],[573,2151],{"className":2152,"style":1464},[897],[573,2154,1192],{"className":2155},[1468],[573,2157],{"className":2158,"style":1464},[897],[573,2160,2162,2165],{"className":2161},[607],[573,2163],{"className":2164,"style":912},[611],[573,2166,1417],{"className":2167},[616],[565,2169,2170,2171,2280,2281,2394,2395,2423,2424,2650,2651,2721,2722,2280,2773,1102],{},"Damit ist ",[573,2172,2174,2204],{"className":2173},[576],[573,2175,2177],{"className":2176},[580],[582,2178,2179],{"xmlns":584},[586,2180,2181,2201],{},[589,2182,2183,2189,2191,2194,2196,2198],{},[789,2184,2185,2187],{},[592,2186,793],{},[810,2188,1417],{},[797,2190,800],{"stretchy":799},[810,2192,2193],{},"3",[797,2195,805],{"stretchy":799},[797,2197,808],{},[810,2199,2200],{},"8",[596,2202,2203],{"encoding":598},"I_1(3) = 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x",[573,3038,3040,3104,3191,3216,3241],{"className":3039,"ariaHidden":603},[602],[573,3041,3043,3046,3086,3089,3092,3095,3098,3101],{"className":3042},[607],[573,3044],{"className":3045,"style":825},[611],[573,3047,3049,3052],{"className":3048},[616],[573,3050,793],{"className":3051,"style":832},[616,617],[573,3053,3055],{"className":3054},[836],[573,3056,3058,3078],{"className":3057},[840,841],[573,3059,3061,3075],{"className":3060},[845],[573,3062,3064],{"className":3063,"style":1869},[849],[573,3065,3066,3069],{"style":853},[573,3067],{"className":3068,"style":858},[857],[573,3070,3072],{"className":3071},[862,863,864,865],[573,3073,812],{"className":3074},[616,865],[573,3076,873],{"className":3077},[872],[573,3079,3081],{"className":3080},[845],[573,3082,3084],{"className":3083,"style":880},[849],[573,3085],{},[573,3087,800],{"className":3088},[886],[573,3090,633],{"className":3091},[616,617],[573,3093,805],{"className":3094},[893],[573,3096],{"className":3097,"style":898},[897],[573,3099,808],{"className":3100},[902],[573,3102],{"className":3103,"style":898},[897],[573,3105,3107,3110,3161,3164,3167,3170,3173,3176,3179,3182,3185,3188],{"className":3106},[607],[573,3108],{"className":3109,"style":1916},[611],[573,3111,3113,3116],{"className":3112},[1306],[573,3114,1197],{"className":3115,"style":1924},[1306,1310,1923],[573,3117,3119],{"className":3118},[836],[573,3120,3122,3153],{"className":3121},[840,841],[573,3123,3125,3150],{"className":3124},[845],[573,3126,3128,3139],{"className":3127,"style":1937},[849],[573,3129,3130,3133],{"style":1940},[573,3131],{"className":3132,"style":858},[857],[573,3134,3136],{"className":3135},[862,863,864,865],[573,3137,812],{"className":3138},[616,865],[573,3140,3141,3144],{"style":1952},[573,3142],{"className":3143,"style":858},[857],[573,3145,3147],{"className":3146},[862,863,864,865],[573,3148,633],{"className":3149},[616,617,865],[573,3151,873],{"className":3152},[872],[573,3154,3156],{"className":3155},[845],[573,3157,3159],{"className":3158,"style":1971},[849],[573,3160],{},[573,3162],{"className":3163,"style":1302},[897],[573,3165,2855],{"className":3166},[1306],[573,3168],{"className":3169,"style":1302},[897],[573,3171,721],{"className":3172},[616,617],[573,3174],{"className":3175,"style":1302},[897],[573,3177,1216],{"className":3178},[616,617],[573,3180,721],{"className":3181},[616,617],[573,3183],{"className":3184,"style":898},[897],[573,3186,808],{"className":3187},[902],[573,3189],{"className":3190,"style":898},[897],[573,3192,3194,3198,3201,3204,3207,3210,3213],{"className":3193},[607],[573,3195],{"className":3196,"style":3197},[611],"height:0.7512em;vertical-align:-0.0833em;",[573,3199,3013],{"className":3200},[1306],[573,3202],{"className":3203,"style":1302},[897],[573,3205,633],{"className":3206},[616,617],[573,3208],{"className":3209,"style":1464},[897],[573,3211,1192],{"className":3212},[1468],[573,3214],{"className":3215,"style":1464},[897],[573,3217,3219,3223,3226,3229,3232,3235,3238],{"className":3218},[607],[573,3220],{"className":3221,"style":3222},[611],"height:0.6679em;",[573,3224,3013],{"className":3225},[1306],[573,3227],{"className":3228,"style":1302},[897],[573,3230,812],{"className":3231},[616],[573,3233],{"className":3234,"style":898},[897],[573,3236,808],{"className":3237},[902],[573,3239],{"className":3240,"style":898},[897],[573,3242,3244,3247,3250,3253],{"className":3243},[607],[573,3245],{"className":3246,"style":3222},[611],[573,3248,3013],{"className":3249},[1306],[573,3251],{"className":3252,"style":1302},[897],[573,3254,633],{"className":3255},[616,617],[565,3257,3258,3259,1102],{},"Zum Beispiel ist ",[573,3260,3262,3301],{"className":3261},[576],[573,3263,3265],{"className":3264},[580],[582,3266,3267],{"xmlns":584},[586,3268,3269,3298],{},[589,3270,3271,3277,3280,3294,3296],{},[789,3272,3273,3275],{},[592,3274,793],{},[810,3276,812],{},[1211,3278,3279],{}," ⁣",[589,3281,3282,3284,3292],{},[797,3283,800],{"fence":603},[3285,3286,3287,3290],"mfrac",{},[592,3288,3289],{},"π",[810,3291,1411],{},[797,3293,805],{"fence":603},[797,3295,808],{},[810,3297,1417],{},[596,3299,3300],{"encoding":598},"I_0\\!\\left(\\frac{\\pi}{2}\\right) = 1",[573,3302,3304,3464],{"className":3303,"ariaHidden":603},[602],[573,3305,3307,3311,3351,3355,3358,3455,3458,3461],{"className":3306},[607],[573,3308],{"className":3309,"style":3310},[611],"height:1.2em;vertical-align:-0.35em;",[573,3312,3314,3317],{"className":3313},[616],[573,3315,793],{"className":3316,"style":832},[616,617],[573,3318,3320],{"className":3319},[836],[573,3321,3323,3343],{"className":3322},[840,841],[573,3324,3326,3340],{"className":3325},[845],[573,3327,3329],{"className":3328,"style":1869},[849],[573,3330,3331,3334],{"style":853},[573,3332],{"className":3333,"style":858},[857],[573,3335,3337],{"className":3336},[862,863,864,865],[573,3338,812],{"className":3339},[616,865],[573,3341,873],{"className":3342},[872],[573,3344,3346],{"className":3345},[845],[573,3347,3349],{"className":3348,"style":880},[849],[573,3350],{},[573,3352],{"className":3353,"style":3354},[897],"margin-right:-0.1667em;",[573,3356],{"className":3357,"style":1302},[897],[573,3359,3362,3371,3449],{"className":3360},[3361],"minner",[573,3363,3367],{"className":3364,"style":3366},[886,3365],"delimcenter","top:0em;",[573,3368,800],{"className":3369},[2014,3370],"size1",[573,3372,3374,3378,3446],{"className":3373},[616],[573,3375],{"className":3376},[886,3377],"nulldelimiter",[573,3379,3381],{"className":3380},[3285],[573,3382,3384,3437],{"className":3383},[840,841],[573,3385,3387,3434],{"className":3386},[845],[573,3388,3391,3407,3418],{"className":3389,"style":3390},[849],"height:0.6954em;",[573,3392,3394,3398],{"style":3393},"top:-2.655em;",[573,3395],{"className":3396,"style":3397},[857],"height:3em;",[573,3399,3401],{"className":3400},[862,863,864,865],[573,3402,3404],{"className":3403},[616,865],[573,3405,1411],{"className":3406},[616,865],[573,3408,3410,3413],{"style":3409},"top:-3.23em;",[573,3411],{"className":3412,"style":3397},[857],[573,3414],{"className":3415,"style":3417},[3416],"frac-line","border-bottom-width:0.04em;",[573,3419,3421,3424],{"style":3420},"top:-3.394em;",[573,3422],{"className":3423,"style":3397},[857],[573,3425,3427],{"className":3426},[862,863,864,865],[573,3428,3430],{"className":3429},[616,865],[573,3431,3289],{"className":3432,"style":3433},[616,617,865],"margin-right:0.0359em;",[573,3435,873],{"className":3436},[872],[573,3438,3440],{"className":3439},[845],[573,3441,3444],{"className":3442,"style":3443},[849],"height:0.345em;",[573,3445],{},[573,3447],{"className":3448},[893,3377],[573,3450,3452],{"className":3451,"style":3366},[893,3365],[573,3453,805],{"className":3454},[2014,3370],[573,3456],{"className":3457,"style":898},[897],[573,3459,808],{"className":3460},[902],[573,3462],{"className":3463,"style":898},[897],[573,3465,3467,3470],{"className":3466},[607],[573,3468],{"className":3469,"style":912},[611],[573,3471,1417],{"className":3472},[616],[560,3474,3476],{"id":3475},"typische-fehler","Typische Fehler",[771,3478,3479,3727,3730],{},[774,3480,3481,3482,3645,3646,1102],{},"Die untere Grenze nicht einsetzen: ",[573,3483,3485,3523],{"className":3484},[576],[573,3486,3488],{"className":3487},[580],[582,3489,3490],{"xmlns":584},[586,3491,3492,3520],{},[589,3493,3494,3502,3504,3506,3508,3510,3512,3514],{},[932,3495,3496,3498,3500],{},[797,3497,1197],{},[810,3499,1417],{},[592,3501,633],{},[810,3503,1411],{},[592,3505,721],{},[1211,3507,1213],{},[592,3509,1216],{},[592,3511,721],{},[797,3513,808],{},[1405,3515,3516,3518],{},[592,3517,633],{},[810,3519,1411],{},[596,3521,3522],{"encoding":598},"\\int_1^x 2t\\,dt = x^2",[573,3524,3526,3610],{"className":3525,"ariaHidden":603},[602],[573,3527,3529,3532,3583,3586,3589,3592,3595,3598,3601,3604,3607],{"className":3528},[607],[573,3530],{"className":3531,"style":1295},[611],[573,3533,3535,3538],{"className":3534},[1306],[573,3536,1197],{"className":3537,"style":1312},[1306,1310,1311],[573,3539,3541],{"className":3540},[836],[573,3542,3544,3575],{"className":3543},[840,841],[573,3545,3547,3572],{"className":3546},[845],[573,3548,3550,3561],{"className":3549,"style":1325},[849],[573,3551,3552,3555],{"style":1328},[573,3553],{"className":3554,"style":858},[857],[573,3556,3558],{"className":3557},[862,863,864,865],[573,3559,1417],{"className":3560},[616,865],[573,3562,3563,3566],{"style":1340},[573,3564],{"className":3565,"style":858},[857],[573,3567,3569],{"className":3568},[862,863,864,865],[573,3570,633],{"className":3571},[616,617,865],[573,3573,873],{"className":3574},[872],[573,3576,3578],{"className":3577},[845],[573,3579,3581],{"className":3580,"style":1359},[849],[573,3582],{},[573,3584],{"className":3585,"style":1302},[897],[573,3587,1411],{"className":3588},[616],[573,3590,721],{"className":3591},[616,617],[573,3593],{"className":3594,"style":1302},[897],[573,3596,1216],{"className":3597},[616,617],[573,3599,721],{"className":3600},[616,617],[573,3602],{"className":3603,"style":898},[897],[573,3605,808],{"className":3606},[902],[573,3608],{"className":3609,"style":898},[897],[573,3611,3613,3616],{"className":3612},[607],[573,3614],{"className":3615,"style":1449},[611],[573,3617,3619,3622],{"className":3618},[616],[573,3620,633],{"className":3621},[616,617],[573,3623,3625],{"className":3624},[836],[573,3626,3628],{"className":3627},[840],[573,3629,3631],{"className":3630},[845],[573,3632,3634],{"className":3633,"style":1449},[849],[573,3635,3636,3639],{"style":1006},[573,3637],{"className":3638,"style":858},[857],[573,3640,3642],{"className":3641},[862,863,864,865],[573,3643,1411],{"className":3644},[616,865]," ist falsch, richtig ist ",[573,3647,3649,3671],{"className":3648},[576],[573,3650,3652],{"className":3651},[580],[582,3653,3654],{"xmlns":584},[586,3655,3656,3668],{},[589,3657,3658,3664,3666],{},[1405,3659,3660,3662],{},[592,3661,633],{},[810,3663,1411],{},[797,3665,1192],{},[810,3667,1417],{},[596,3669,3670],{"encoding":598},"x^2 - 1",[573,3672,3674,3718],{"className":3673,"ariaHidden":603},[602],[573,3675,3677,3680,3709,3712,3715],{"className":3676},[607],[573,3678],{"className":3679,"style":1430},[611],[573,3681,3683,3686],{"className":3682},[616],[573,3684,633],{"className":3685},[616,617],[573,3687,3689],{"className":3688},[836],[573,3690,3692],{"className":3691},[840],[573,3693,3695],{"className":3694},[845],[573,3696,3698],{"className":3697,"style":1449},[849],[573,3699,3700,3703],{"style":1006},[573,3701],{"className":3702,"style":858},[857],[573,3704,3706],{"className":3705},[862,863,864,865],[573,3707,1411],{"className":3708},[616,865],[573,3710],{"className":3711,"style":1464},[897],[573,3713,1192],{"className":3714},[1468],[573,3716],{"className":3717,"style":1464},[897],[573,3719,3721,3724],{"className":3720},[607],[573,3722],{"className":3723,"style":912},[611],[573,3725,1417],{"className":3726},[616],[774,3728,3729],{},"Die Integrationsvariable und die obere Grenze gleich benennen. Das führt beim Ableiten und Einsetzen zu Verwechslungen.",[774,3731,3732,3733,3761,3762,3899],{},"Beim Ableiten den Hauptsatz übersehen und die Integralfunktion erst ausrechnen. Für stetiges ",[573,3734,3736,3749],{"className":3735},[576],[573,3737,3739],{"className":3738},[580],[582,3740,3741],{"xmlns":584},[586,3742,3743,3747],{},[589,3744,3745],{},[592,3746,953],{},[596,3748,953],{"encoding":598},[573,3750,3752],{"className":3751,"ariaHidden":603},[602],[573,3753,3755,3758],{"className":3754},[607],[573,3756],{"className":3757,"style":1098},[611],[573,3759,953],{"className":3760,"style":1058},[616,617]," ist ",[573,3763,3765,3800],{"className":3764},[576],[573,3766,3768],{"className":3767},[580],[582,3769,3770],{"xmlns":584},[586,3771,3772,3798],{},[589,3773,3774,3782,3784,3786,3788,3790,3792,3794,3796],{},[932,3775,3776,3778,3780],{},[592,3777,793],{},[592,3779,594],{},[797,3781,942],{"mathvariant":940,"lspace":941,"rspace":941},[797,3783,800],{"stretchy":799},[592,3785,633],{},[797,3787,805],{"stretchy":799},[797,3789,808],{},[592,3791,953],{},[797,3793,800],{"stretchy":799},[592,3795,633],{},[797,3797,805],{"stretchy":799},[596,3799,962],{"encoding":598},[573,3801,3803,3881],{"className":3802,"ariaHidden":603},[602],[573,3804,3806,3809,3863,3866,3869,3872,3875,3878],{"className":3805},[607],[573,3807],{"className":3808,"style":972},[611],[573,3810,3812,3815],{"className":3811},[616],[573,3813,793],{"className":3814,"style":832},[616,617],[573,3816,3818],{"className":3817},[836],[573,3819,3821,3855],{"className":3820},[840,841],[573,3822,3824,3852],{"className":3823},[845],[573,3825,3827,3838],{"className":3826,"style":991},[849],[573,3828,3829,3832],{"style":994},[573,3830],{"className":3831,"style":858},[857],[573,3833,3835],{"className":3834},[862,863,864,865],[573,3836,594],{"className":3837},[616,617,865],[573,3839,3840,3843],{"style":1006},[573,3841],{"className":3842,"style":858},[857],[573,3844,3846],{"className":3845},[862,863,864,865],[573,3847,3849],{"className":3848},[616,865],[573,3850,942],{"className":3851},[616,865],[573,3853,873],{"className":3854},[872],[573,3856,3858],{"className":3857},[845],[573,3859,3861],{"className":3860,"style":1028},[849],[573,3862],{},[573,3864,800],{"className":3865},[886],[573,3867,633],{"className":3868},[616,617],[573,3870,805],{"className":3871},[893],[573,3873],{"className":3874,"style":898},[897],[573,3876,808],{"className":3877},[902],[573,3879],{"className":3880,"style":898},[897],[573,3882,3884,3887,3890,3893,3896],{"className":3883},[607],[573,3885],{"className":3886,"style":825},[611],[573,3888,953],{"className":3889,"style":1058},[616,617],[573,3891,800],{"className":3892},[886],[573,3894,633],{"className":3895},[616,617],[573,3897,805],{"className":3898},[893]," direkt ablesbar.",{"title":3901,"searchDepth":3902,"depth":3902,"links":3903},"",2,[3904,3905,3906],{"id":562,"depth":3902,"text":563},{"id":1628,"depth":3902,"text":1629},{"id":3475,"depth":3902,"text":3476},[3908,3910,3912,3914,3917,3919,3921,3924],{"lhs":3909,"rhs":3670},"x^2 - 1^2",{"lhs":3911,"rhs":2200},"3^2 - 1",{"lhs":3913,"rhs":2200},"round(sum(map(0:999, f(k) = 2*(1 + (k + 0.5)*2\u002F1000))) * 2\u002F1000, 6)",{"lhs":3915,"rhs":3916},"0^2 - 1","-1",{"lhs":3918,"rhs":1417},"round(sum(map(0:999, f(k) = 2*(k + 0.5)\u002F1000)) \u002F 1000, 6)",{"lhs":3920,"rhs":812},"(-1)^2 - 1",{"lhs":3922,"rhs":3923},"round(sum(map(0:999, f(k) = cos((k + 0.5)*pi\u002F2\u002F1000))) * pi\u002F2\u002F1000, 4)","sin(pi\u002F2)",{"lhs":3925,"rhs":3926},"(x^2 - u^2) - (x^2 - v^2)","v^2 - u^2","f \\text{ stetig auf einem Intervall, das } a \\text{ und } x \\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>\u003C\u002Fmrow>\u003Cannotation 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