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durch ",[572,996,998,1011],{"className":997},[575],[572,999,1001],{"className":1000},[579],[581,1002,1003],{"xmlns":583},[585,1004,1005,1009],{},[588,1006,1007],{},[595,1008,769],{"mathvariant":768},[603,1010,912],{"encoding":605},[572,1012,1014],{"className":1013,"ariaHidden":593},[610],[572,1015,1017,1020],{"className":1016},[614],[572,1018],{"className":1019,"style":922},[618],[572,1021,769],{"className":1022},[623]," auf ein kleines Parallelotop abgebildet, dessen Volumen um den Faktor ",[572,1025,1027,1058],{"className":1026},[575],[572,1028,1030],{"className":1029},[579],[581,1031,1032],{"xmlns":583},[585,1033,1034,1055],{},[588,1035,1036,1039,1042,1045,1053],{},[595,1037,1038],{"mathvariant":768},"∣",[595,1040,1041],{},"det",[599,1043,1044],{},"⁡",[1046,1047,1048,1051],"msub",{},[595,1049,1050],{},"J",[595,1052,769],{"mathvariant":768},[595,1054,1038],{"mathvariant":768},[603,1056,1057],{"encoding":605},"|\\det J_\\Phi|",[572,1059,1061],{"className":1060,"ariaHidden":593},[610],[572,1062,1064,1067,1070,1074,1078,1081,1134],{"className":1063},[614],[572,1065],{"className":1066,"style":848},[618],[572,1068,1038],{"className":1069},[623],[572,1071],{"className":1072,"style":1073},[833],"margin-right:0.1667em;",[572,1075,1041],{"className":1076},[1077],"mop",[572,1079],{"className":1080,"style":1073},[833],[572,1082,1084,1088],{"className":1083},[623],[572,1085,1050],{"className":1086,"style":1087},[623,648],"margin-right:0.0962em;",[572,1089,1092],{"className":1090},[1091],"msupsub",[572,1093,1096,1125],{"className":1094},[628,1095],"vlist-t2",[572,1097,1099,1120],{"className":1098},[632],[572,1100,1103],{"className":1101,"style":1102},[636],"height:0.3283em;",[572,1104,1106,1110],{"style":1105},"top:-2.55em;margin-left:-0.0962em;margin-right:0.05em;",[572,1107],{"className":1108,"style":1109},[643],"height:2.7em;",[572,1111,1117],{"className":1112},[1113,1114,1115,1116],"sizing","reset-size6","size3","mtight",[572,1118,769],{"className":1119},[623,1116],[572,1121,1124],{"className":1122},[1123],"vlist-s","​",[572,1126,1128],{"className":1127},[632],[572,1129,1132],{"className":1130,"style":1131},[636],"height:0.15em;",[572,1133],{},[572,1135,1038],{"className":1136},[623]," größer oder kleiner ist. Deshalb steht der ",[568,1139,1140],{},"Betrag der Jacobi-Determinante"," im Integral. Er ersetzt den Faktor ",[572,1143,1145,1178],{"className":1144},[575],[572,1146,1148],{"className":1147},[579],[581,1149,1150],{"xmlns":583},[585,1151,1152,1175],{},[588,1153,1154,1156,1166,1168,1171,1173],{},[595,1155,1038],{"mathvariant":768},[1157,1158,1159,1162],"msup",{},[595,1160,1161],{},"φ",[599,1163,1165],{"mathvariant":768,"lspace":1164,"rspace":1164},"0em","′",[599,1167,773],{"stretchy":772},[595,1169,1170],{},"t",[599,1172,782],{"stretchy":772},[595,1174,1038],{"mathvariant":768},[603,1176,1177],{"encoding":605},"|\\varphi'(t)|",[572,1179,1181],{"className":1180,"ariaHidden":593},[610],[572,1182,1184,1188,1191,1225,1228,1231,1234],{"className":1183},[614],[572,1185],{"className":1186,"style":1187},[618],"height:1.0019em;vertical-align:-0.25em;",[572,1189,1038],{"className":1190},[623],[572,1192,1194,1197],{"className":1193},[623],[572,1195,1161],{"className":1196},[623,648],[572,1198,1200],{"className":1199},[1091],[572,1201,1203],{"className":1202},[628],[572,1204,1206],{"className":1205},[632],[572,1207,1210],{"className":1208,"style":1209},[636],"height:0.7519em;",[572,1211,1213,1216],{"style":1212},"top:-3.063em;margin-right:0.05em;",[572,1214],{"className":1215,"style":1109},[643],[572,1217,1219],{"className":1218},[1113,1114,1115,1116],[572,1220,1222],{"className":1221},[623,1116],[572,1223,1165],{"className":1224},[623,1116],[572,1226,773],{"className":1227},[855],[572,1229,1170],{"className":1230},[623,648],[572,1232,782],{"className":1233},[894],[572,1235,1038],{"className":1236},[623]," der eindimensionalen Regel.",[564,1239,1240],{},"Wichtige Sonderfälle:",[1242,1243,1244,1325,1401,1531],"ul",{},[1245,1246,1247,1248],"li",{},"Polarkoordinaten: ",[572,1249,1251,1278],{"className":1250},[575],[572,1252,1254],{"className":1253},[579],[581,1255,1256],{"xmlns":583},[585,1257,1258,1275],{},[588,1259,1260,1262,1264,1266,1268,1270,1272],{},[595,1261,1038],{"mathvariant":768},[595,1263,1041],{},[599,1265,1044],{},[595,1267,1050],{},[595,1269,1038],{"mathvariant":768},[599,1271,765],{},[595,1273,1274],{},"r",[603,1276,1277],{"encoding":605},"|\\det J| = r",[572,1279,1281,1314],{"className":1280,"ariaHidden":593},[610],[572,1282,1284,1287,1290,1293,1296,1299,1302,1305,1308,1311],{"className":1283},[614],[572,1285],{"className":1286,"style":848},[618],[572,1288,1038],{"className":1289},[623],[572,1291],{"className":1292,"style":1073},[833],[572,1294,1041],{"className":1295},[1077],[572,1297],{"className":1298,"style":1073},[833],[572,1300,1050],{"className":1301,"style":1087},[623,648],[572,1303,1038],{"className":1304},[623],[572,1306],{"className":1307,"style":834},[833],[572,1309,765],{"className":1310},[838],[572,1312],{"className":1313,"style":834},[833],[572,1315,1317,1321],{"className":1316},[614],[572,1318],{"className":1319,"style":1320},[618],"height:0.4306em;",[572,1322,1274],{"className":1323,"style":1324},[623,648],"margin-right:0.0278em;",[1245,1326,1327,1328],{},"Zylinderkoordinaten: ",[572,1329,1331,1356],{"className":1330},[575],[572,1332,1334],{"className":1333},[579],[581,1335,1336],{"xmlns":583},[585,1337,1338,1354],{},[588,1339,1340,1342,1344,1346,1348,1350,1352],{},[595,1341,1038],{"mathvariant":768},[595,1343,1041],{},[599,1345,1044],{},[595,1347,1050],{},[595,1349,1038],{"mathvariant":768},[599,1351,765],{},[595,1353,1274],{},[603,1355,1277],{"encoding":605},[572,1357,1359,1392],{"className":1358,"ariaHidden":593},[610],[572,1360,1362,1365,1368,1371,1374,1377,1380,1383,1386,1389],{"className":1361},[614],[572,1363],{"className":1364,"style":848},[618],[572,1366,1038],{"className":1367},[623],[572,1369],{"className":1370,"style":1073},[833],[572,1372,1041],{"className":1373},[1077],[572,1375],{"className":1376,"style":1073},[833],[572,1378,1050],{"className":1379,"style":1087},[623,648],[572,1381,1038],{"className":1382},[623],[572,1384],{"className":1385,"style":834},[833],[572,1387,765],{"className":1388},[838],[572,1390],{"className":1391,"style":834},[833],[572,1393,1395,1398],{"className":1394},[614],[572,1396],{"className":1397,"style":1320},[618],[572,1399,1274],{"className":1400,"style":1324},[623,648],[1245,1402,1403,1404],{},"Kugelkoordinaten: ",[572,1405,1407,1447],{"className":1406},[575],[572,1408,1410],{"className":1409},[579],[581,1411,1412],{"xmlns":583},[585,1413,1414,1444],{},[588,1415,1416,1418,1420,1422,1424,1426,1428,1436,1439,1441],{},[595,1417,1038],{"mathvariant":768},[595,1419,1041],{},[599,1421,1044],{},[595,1423,1050],{},[595,1425,1038],{"mathvariant":768},[599,1427,765],{},[1157,1429,1430,1432],{},[595,1431,1274],{},[1433,1434,1435],"mn",{},"2",[595,1437,1438],{},"sin",[599,1440,1044],{},[595,1442,1443],{},"θ",[603,1445,1446],{"encoding":605},"|\\det J| = r^2 \\sin\\theta",[572,1448,1450,1483],{"className":1449,"ariaHidden":593},[610],[572,1451,1453,1456,1459,1462,1465,1468,1471,1474,1477,1480],{"className":1452},[614],[572,1454],{"className":1455,"style":848},[618],[572,1457,1038],{"className":1458},[623],[572,1460],{"className":1461,"style":1073},[833],[572,1463,1041],{"className":1464},[1077],[572,1466],{"className":1467,"style":1073},[833],[572,1469,1050],{"className":1470,"style":1087},[623,648],[572,1472,1038],{"className":1473},[623],[572,1475],{"className":1476,"style":834},[833],[572,1478,765],{"className":1479},[838],[572,1481],{"className":1482,"style":834},[833],[572,1484,1486,1490,1519,1522,1525,1528],{"className":1485},[614],[572,1487],{"className":1488,"style":1489},[618],"height:0.8141em;",[572,1491,1493,1496],{"className":1492},[623],[572,1494,1274],{"className":1495,"style":1324},[623,648],[572,1497,1499],{"className":1498},[1091],[572,1500,1502],{"className":1501},[628],[572,1503,1505],{"className":1504},[632],[572,1506,1508],{"className":1507,"style":1489},[636],[572,1509,1510,1513],{"style":1212},[572,1511],{"className":1512,"style":1109},[643],[572,1514,1516],{"className":1515},[1113,1114,1115,1116],[572,1517,1435],{"className":1518},[623,1116],[572,1520],{"className":1521,"style":1073},[833],[572,1523,1438],{"className":1524},[1077],[572,1526],{"className":1527,"style":1073},[833],[572,1529,1443],{"className":1530,"style":1324},[623,648],[1245,1532,1533,1534,1663,1664],{},"Lineare Abbildung ",[572,1535,1537,1566],{"className":1536},[575],[572,1538,1540],{"className":1539},[579],[581,1541,1542],{"xmlns":583},[585,1543,1544,1563],{},[588,1545,1546,1552,1554,1557],{},[591,1547,1548,1550],{"accent":593},[595,1549,597],{},[599,1551,601],{},[599,1553,765],{},[595,1555,1556],{},"A",[591,1558,1559,1561],{"accent":593},[595,1560,694],{},[599,1562,601],{},[603,1564,1565],{"encoding":605},"\\vec x = A \\vec u",[572,1567,1569,1619],{"className":1568,"ariaHidden":593},[610],[572,1570,1572,1575,1610,1613,1616],{"className":1571},[614],[572,1573],{"className":1574,"style":619},[618],[572,1576,1578],{"className":1577},[623,624],[572,1579,1581],{"className":1580},[628],[572,1582,1584],{"className":1583},[632],[572,1585,1587,1595],{"className":1586,"style":619},[636],[572,1588,1589,1592],{"style":639},[572,1590],{"className":1591,"style":644},[643],[572,1593,597],{"className":1594},[623,648],[572,1596,1597,1600],{"style":639},[572,1598],{"className":1599,"style":644},[643],[572,1601,1603],{"className":1602,"style":658},[657],[572,1604,1606],{"className":1605,"style":663},[662],[665,1607,1608],{"xmlns":667,"width":668,"height":669,"style":670,"viewBox":671,"preserveAspectRatio":672},[674,1609],{"d":676},[572,1611],{"className":1612,"style":834},[833],[572,1614,765],{"className":1615},[838],[572,1617],{"className":1618,"style":834},[833],[572,1620,1622,1625,1628],{"className":1621},[614],[572,1623],{"className":1624,"style":619},[618],[572,1626,1556],{"className":1627},[623,648],[572,1629,1631],{"className":1630},[623,624],[572,1632,1634],{"className":1633},[628],[572,1635,1637],{"className":1636},[632],[572,1638,1640,1648],{"className":1639,"style":619},[636],[572,1641,1642,1645],{"style":639},[572,1643],{"className":1644,"style":644},[643],[572,1646,694],{"className":1647},[623,648],[572,1649,1650,1653],{"style":639},[572,1651],{"className":1652,"style":644},[643],[572,1654,1656],{"className":1655,"style":658},[657],[572,1657,1659],{"className":1658,"style":663},[662],[665,1660,1661],{"xmlns":667,"width":668,"height":669,"style":670,"viewBox":671,"preserveAspectRatio":672},[674,1662],{"d":676},": ",[572,1665,1667,1701],{"className":1666},[575],[572,1668,1670],{"className":1669},[579],[581,1671,1672],{"xmlns":583},[585,1673,1674,1698],{},[588,1675,1676,1678,1680,1682,1684,1686,1688,1690,1692,1694,1696],{},[595,1677,1038],{"mathvariant":768},[595,1679,1041],{},[599,1681,1044],{},[595,1683,1050],{},[595,1685,1038],{"mathvariant":768},[599,1687,765],{},[595,1689,1038],{"mathvariant":768},[595,1691,1041],{},[599,1693,1044],{},[595,1695,1556],{},[595,1697,1038],{"mathvariant":768},[603,1699,1700],{"encoding":605},"|\\det J| = |\\det A|",[572,1702,1704,1737],{"className":1703,"ariaHidden":593},[610],[572,1705,1707,1710,1713,1716,1719,1722,1725,1728,1731,1734],{"className":1706},[614],[572,1708],{"className":1709,"style":848},[618],[572,1711,1038],{"className":1712},[623],[572,1714],{"className":1715,"style":1073},[833],[572,1717,1041],{"className":1718},[1077],[572,1720],{"className":1721,"style":1073},[833],[572,1723,1050],{"className":1724,"style":1087},[623,648],[572,1726,1038],{"className":1727},[623],[572,1729],{"className":1730,"style":834},[833],[572,1732,765],{"className":1733},[838],[572,1735],{"className":1736,"style":834},[833],[572,1738,1740,1743,1746,1749,1752,1755,1758],{"className":1739},[614],[572,1741],{"className":1742,"style":848},[618],[572,1744,1038],{"className":1745},[623],[572,1747],{"className":1748,"style":1073},[833],[572,1750,1041],{"className":1751},[1077],[572,1753],{"className":1754,"style":1073},[833],[572,1756,1556],{"className":1757},[623,648],[572,1759,1038],{"className":1760},[623],[564,1762,1763,1764,1792],{},"Mengen vom Volumen null (z.B. Randkurven oder die Achse bei Polarkoordinaten) dürfen ausgenommen werden; dort darf ",[572,1765,1767,1780],{"className":1766},[575],[572,1768,1770],{"className":1769},[579],[581,1771,1772],{"xmlns":583},[585,1773,1774,1778],{},[588,1775,1776],{},[595,1777,769],{"mathvariant":768},[603,1779,912],{"encoding":605},[572,1781,1783],{"className":1782,"ariaHidden":593},[610],[572,1784,1786,1789],{"className":1785},[614],[572,1787],{"className":1788,"style":922},[618],[572,1790,769],{"className":1791},[623]," die Voraussetzungen verletzen.",[559,1794,1796],{"id":1795},"beispiele","Beispiele",[564,1798,1799,1800,1829,1830,1860,1861,1917,1918,1978,1979,2043],{},"Die Ellipse mit den Halbachsen ",[572,1801,1803,1817],{"className":1802},[575],[572,1804,1806],{"className":1805},[579],[581,1807,1808],{"xmlns":583},[585,1809,1810,1815],{},[588,1811,1812],{},[595,1813,1814],{},"a",[603,1816,1814],{"encoding":605},[572,1818,1820],{"className":1819,"ariaHidden":593},[610],[572,1821,1823,1826],{"className":1822},[614],[572,1824],{"className":1825,"style":1320},[618],[572,1827,1814],{"className":1828},[623,648]," und ",[572,1831,1833,1847],{"className":1832},[575],[572,1834,1836],{"className":1835},[579],[581,1837,1838],{"xmlns":583},[585,1839,1840,1845],{},[588,1841,1842],{},[595,1843,1844],{},"b",[603,1846,1844],{"encoding":605},[572,1848,1850],{"className":1849,"ariaHidden":593},[610],[572,1851,1853,1857],{"className":1852},[614],[572,1854],{"className":1855,"style":1856},[618],"height:0.6944em;",[572,1858,1844],{"className":1859},[623,648]," ist das Bild der Einheitskreisscheibe unter ",[572,1862,1864,1884],{"className":1863},[575],[572,1865,1867],{"className":1866},[579],[581,1868,1869],{"xmlns":583},[585,1870,1871,1881],{},[588,1872,1873,1875,1877,1879],{},[595,1874,597],{},[599,1876,765],{},[595,1878,1814],{},[595,1880,694],{},[603,1882,1883],{"encoding":605},"x = au",[572,1885,1887,1905],{"className":1886,"ariaHidden":593},[610],[572,1888,1890,1893,1896,1899,1902],{"className":1889},[614],[572,1891],{"className":1892,"style":1320},[618],[572,1894,597],{"className":1895},[623,648],[572,1897],{"className":1898,"style":834},[833],[572,1900,765],{"className":1901},[838],[572,1903],{"className":1904,"style":834},[833],[572,1906,1908,1911,1914],{"className":1907},[614],[572,1909],{"className":1910,"style":1320},[618],[572,1912,1814],{"className":1913},[623,648],[572,1915,694],{"className":1916},[623,648],", ",[572,1919,1921,1943],{"className":1920},[575],[572,1922,1924],{"className":1923},[579],[581,1925,1926],{"xmlns":583},[585,1927,1928,1940],{},[588,1929,1930,1933,1935,1937],{},[595,1931,1932],{},"y",[599,1934,765],{},[595,1936,1844],{},[595,1938,1939],{},"v",[603,1941,1942],{"encoding":605},"y = bv",[572,1944,1946,1966],{"className":1945,"ariaHidden":593},[610],[572,1947,1949,1953,1957,1960,1963],{"className":1948},[614],[572,1950],{"className":1951,"style":1952},[618],"height:0.625em;vertical-align:-0.1944em;",[572,1954,1932],{"className":1955,"style":1956},[623,648],"margin-right:0.0359em;",[572,1958],{"className":1959,"style":834},[833],[572,1961,765],{"className":1962},[838],[572,1964],{"className":1965,"style":834},[833],[572,1967,1969,1972,1975],{"className":1968},[614],[572,1970],{"className":1971,"style":1856},[618],[572,1973,1844],{"className":1974},[623,648],[572,1976,1939],{"className":1977,"style":1956},[623,648],". Mit ",[572,1980,1982,2006],{"className":1981},[575],[572,1983,1985],{"className":1984},[579],[581,1986,1987],{"xmlns":583},[585,1988,1989,2003],{},[588,1990,1991,1993,1995,1997,1999,2001],{},[595,1992,1041],{},[599,1994,1044],{},[595,1996,1050],{},[599,1998,765],{},[595,2000,1814],{},[595,2002,1844],{},[603,2004,2005],{"encoding":605},"\\det J = ab",[572,2007,2009,2033],{"className":2008,"ariaHidden":593},[610],[572,2010,2012,2015,2018,2021,2024,2027,2030],{"className":2011},[614],[572,2013],{"className":2014,"style":1856},[618],[572,2016,1041],{"className":2017},[1077],[572,2019],{"className":2020,"style":1073},[833],[572,2022,1050],{"className":2023,"style":1087},[623,648],[572,2025],{"className":2026,"style":834},[833],[572,2028,765],{"className":2029},[838],[572,2031],{"className":2032,"style":834},[833],[572,2034,2036,2039],{"className":2035},[614],[572,2037],{"className":2038,"style":1856},[618],[572,2040,2042],{"className":2041},[623,648],"ab",":",[572,2045,2048],{"className":2046},[2047],"katex-display",[572,2049,2051,2147],{"className":2050},[575],[572,2052,2054],{"className":2053},[579],[581,2055,2057],{"xmlns":583,"display":2056},"block",[585,2058,2059,2144],{},[588,2060,2061,2063,2065,2074,2077,2080,2083,2085,2087,2089,2091,2093,2119,2121,2123,2125,2127,2129,2131,2133,2135,2137,2140,2142],{},[595,2062,1556],{},[599,2064,765],{},[1046,2066,2067,2070],{},[599,2068,2069],{},"∬",[2071,2072,2073],"mtext",{},"Ellipse",[1433,2075,2076],{},"1",[2071,2078,2079],{}," ",[595,2081,2082],{},"d",[595,2084,597],{},[2071,2086,2079],{},[595,2088,2082],{},[595,2090,1932],{},[599,2092,765],{},[1046,2094,2095,2097],{},[599,2096,2069],{},[588,2098,2099,2105,2108,2114,2117],{},[1157,2100,2101,2103],{},[595,2102,694],{},[1433,2104,1435],{},[599,2106,2107],{},"+",[1157,2109,2110,2112],{},[595,2111,1939],{},[1433,2113,1435],{},[599,2115,2116],{},"≤",[1433,2118,2076],{},[595,2120,1814],{},[595,2122,1844],{},[2071,2124,2079],{},[595,2126,2082],{},[595,2128,694],{},[2071,2130,2079],{},[595,2132,2082],{},[595,2134,1939],{},[599,2136,765],{},[595,2138,2139],{},"π",[595,2141,1814],{},[595,2143,1844],{},[603,2145,2146],{"encoding":605},"A = \\iint_{\\text{Ellipse}} 1\\, dx\\, dy = \\iint_{u^2 + v^2 \\leq 1} ab\\, du\\, dv = \\pi ab",[572,2148,2150,2168,2261,2416],{"className":2149,"ariaHidden":593},[610],[572,2151,2153,2156,2159,2162,2165],{"className":2152},[614],[572,2154],{"className":2155,"style":922},[618],[572,2157,1556],{"className":2158},[623,648],[572,2160],{"className":2161,"style":834},[833],[572,2163,765],{"className":2164},[838],[572,2166],{"className":2167,"style":834},[833],[572,2169,2171,2175,2228,2231,2234,2237,2240,2243,2246,2249,2252,2255,2258],{"className":2170},[614],[572,2172],{"className":2173,"style":2174},[618],"height:2.4078em;vertical-align:-1.0478em;",[572,2176,2178,2184],{"className":2177},[1077],[572,2179,2069],{"className":2180,"style":2183},[1077,2181,2182],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.001em;",[572,2185,2187],{"className":2186},[1091],[572,2188,2190,2219],{"className":2189},[628,1095],[572,2191,2193,2216],{"className":2192},[632],[572,2194,2197],{"className":2195,"style":2196},[636],"height:-0.4256em;",[572,2198,2200,2203],{"style":2199},"top:-1.7883em;margin-left:-0.4445em;margin-right:0.05em;",[572,2201],{"className":2202,"style":1109},[643],[572,2204,2206],{"className":2205},[1113,1114,1115,1116],[572,2207,2209],{"className":2208},[623,1116],[572,2210,2213],{"className":2211},[623,2212,1116],"text",[572,2214,2073],{"className":2215},[623,1116],[572,2217,1124],{"className":2218},[1123],[572,2220,2222],{"className":2221},[632],[572,2223,2226],{"className":2224,"style":2225},[636],"height:1.0478em;",[572,2227],{},[572,2229],{"className":2230,"style":1073},[833],[572,2232,2076],{"className":2233},[623],[572,2235],{"className":2236,"style":1073},[833],[572,2238,2082],{"className":2239},[623,648],[572,2241,597],{"className":2242},[623,648],[572,2244],{"className":2245,"style":1073},[833],[572,2247,2082],{"className":2248},[623,648],[572,2250,1932],{"className":2251,"style":1956},[623,648],[572,2253],{"className":2254,"style":834},[833],[572,2256,765],{"className":2257},[838],[572,2259],{"className":2260,"style":834},[833],[572,2262,2264,2268,2383,2386,2389,2392,2395,2398,2401,2404,2407,2410,2413],{"className":2263},[614],[572,2265],{"className":2266,"style":2267},[618],"height:2.3669em;vertical-align:-1.0069em;",[572,2269,2271,2274],{"className":2270},[1077],[572,2272,2069],{"className":2273,"style":2183},[1077,2181,2182],[572,2275,2277],{"className":2276},[1091],[572,2278,2280,2374],{"className":2279},[628,1095],[572,2281,2283,2371],{"className":2282},[632],[572,2284,2287],{"className":2285,"style":2286},[636],"height:-0.3893em;",[572,2288,2289,2292],{"style":2199},[572,2290],{"className":2291,"style":1109},[643],[572,2293,2295],{"className":2294},[1113,1114,1115,1116],[572,2296,2298,2332,2336,2365,2368],{"className":2297},[623,1116],[572,2299,2301,2304],{"className":2300},[623,1116],[572,2302,694],{"className":2303},[623,648,1116],[572,2305,2307],{"className":2306},[1091],[572,2308,2310],{"className":2309},[628],[572,2311,2313],{"className":2312},[632],[572,2314,2317],{"className":2315,"style":2316},[636],"height:0.7463em;",[572,2318,2320,2324],{"style":2319},"top:-2.786em;margin-right:0.0714em;",[572,2321],{"className":2322,"style":2323},[643],"height:2.5em;",[572,2325,2329],{"className":2326},[1113,2327,2328,1116],"reset-size3","size1",[572,2330,1435],{"className":2331},[623,1116],[572,2333,2107],{"className":2334},[2335,1116],"mbin",[572,2337,2339,2342],{"className":2338},[623,1116],[572,2340,1939],{"className":2341,"style":1956},[623,648,1116],[572,2343,2345],{"className":2344},[1091],[572,2346,2348],{"className":2347},[628],[572,2349,2351],{"className":2350},[632],[572,2352,2354],{"className":2353,"style":2316},[636],[572,2355,2356,2359],{"style":2319},[572,2357],{"className":2358,"style":2323},[643],[572,2360,2362],{"className":2361},[1113,2327,2328,1116],[572,2363,1435],{"className":2364},[623,1116],[572,2366,2116],{"className":2367},[838,1116],[572,2369,2076],{"className":2370},[623,1116],[572,2372,1124],{"className":2373},[1123],[572,2375,2377],{"className":2376},[632],[572,2378,2381],{"className":2379,"style":2380},[636],"height:1.0069em;",[572,2382],{},[572,2384],{"className":2385,"style":1073},[833],[572,2387,2042],{"className":2388},[623,648],[572,2390],{"className":2391,"style":1073},[833],[572,2393,2082],{"className":2394},[623,648],[572,2396,694],{"className":2397},[623,648],[572,2399],{"className":2400,"style":1073},[833],[572,2402,2082],{"className":2403},[623,648],[572,2405,1939],{"className":2406,"style":1956},[623,648],[572,2408],{"className":2409,"style":834},[833],[572,2411,765],{"className":2412},[838],[572,2414],{"className":2415,"style":834},[833],[572,2417,2419,2422,2425],{"className":2418},[614],[572,2420],{"className":2421,"style":1856},[618],[572,2423,2139],{"className":2424,"style":1956},[623,648],[572,2426,2042],{"className":2427},[623,648],[564,2429,2430,2431,2592,2593,744,2621,1829,2705,1978,2789,1829,2863,2936,2937,1829,3079,3211],{},"Gesucht ist ",[572,2432,2434,2473],{"className":2433},[575],[572,2435,2437],{"className":2436},[579],[581,2438,2439],{"xmlns":583},[585,2440,2441,2470],{},[588,2442,2443,2450,2452,2454,2456,2458,2464,2466,2468],{},[1046,2444,2445,2447],{},[599,2446,2069],{},[595,2448,2449],{},"D",[599,2451,773],{"stretchy":772},[595,2453,597],{},[599,2455,2107],{},[595,2457,1932],{},[1157,2459,2460,2462],{},[599,2461,782],{"stretchy":772},[1433,2463,1435],{},[2071,2465,2079],{},[595,2467,2082],{},[595,2469,1556],{},[603,2471,2472],{"encoding":605},"\\iint_D (x + y)^2\\, 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über das gedrehte Quadrat ",[572,2594,2596,2609],{"className":2595},[575],[572,2597,2599],{"className":2598},[579],[581,2600,2601],{"xmlns":583},[585,2602,2603,2607],{},[588,2604,2605],{},[595,2606,2449],{},[603,2608,2449],{"encoding":605},[572,2610,2612],{"className":2611,"ariaHidden":593},[610],[572,2613,2615,2618],{"className":2614},[614],[572,2616],{"className":2617,"style":922},[618],[572,2619,2449],{"className":2620,"style":1324},[623,648],[572,2622,2624,2650],{"className":2623},[575],[572,2625,2627],{"className":2626},[579],[581,2628,2629],{"xmlns":583},[585,2630,2631,2647],{},[588,2632,2633,2635,2637,2639,2641,2643,2645],{},[595,2634,1038],{"mathvariant":768},[595,2636,597],{},[599,2638,2107],{},[595,2640,1932],{},[595,2642,1038],{"mathvariant":768},[599,2644,2116],{},[1433,2646,2076],{},[603,2648,2649],{"encoding":605},"|x + y| \\leq 1",[572,2651,2653,2674,2695],{"className":2652,"ariaHidden":593},[610],[572,2654,2656,2659,2662,2665,2668,2671],{"className":2655},[614],[572,2657],{"className":2658,"style":848},[618],[572,2660,1038],{"className":2661},[623],[572,2663,597],{"className":2664},[623,648],[572,2666],{"className":2667,"style":2537},[833],[572,2669,2107],{"className":2670},[2335],[572,2672],{"className":2673,"style":2537},[833],[572,2675,2677,2680,2683,2686,2689,2692],{"className":2676},[614],[572,2678],{"className":2679,"style":848},[618],[572,2681,1932],{"className":2682,"style":1956},[623,648],[572,2684,1038],{"className":2685},[623],[572,2687],{"className":2688,"style":834},[833],[572,2690,2116],{"className":2691},[838],[572,2693],{"className":2694,"style":834},[833],[572,2696,2698,2702],{"className":2697},[614],[572,2699],{"className":2700,"style":2701},[618],"height:0.6444em;",[572,2703,2076],{"className":2704},[623],[572,2706,2708,2735],{"className":2707},[575],[572,2709,2711],{"className":2710},[579],[581,2712,2713],{"xmlns":583},[585,2714,2715,2732],{},[588,2716,2717,2719,2721,2724,2726,2728,2730],{},[595,2718,1038],{"mathvariant":768},[595,2720,597],{},[599,2722,2723],{},"−",[595,2725,1932],{},[595,2727,1038],{"mathvariant":768},[599,2729,2116],{},[1433,2731,2076],{},[603,2733,2734],{"encoding":605},"|x 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= x + y",[572,2815,2817,2835,2854],{"className":2816,"ariaHidden":593},[610],[572,2818,2820,2823,2826,2829,2832],{"className":2819},[614],[572,2821],{"className":2822,"style":1320},[618],[572,2824,694],{"className":2825},[623,648],[572,2827],{"className":2828,"style":834},[833],[572,2830,765],{"className":2831},[838],[572,2833],{"className":2834,"style":834},[833],[572,2836,2838,2842,2845,2848,2851],{"className":2837},[614],[572,2839],{"className":2840,"style":2841},[618],"height:0.6667em;vertical-align:-0.0833em;",[572,2843,597],{"className":2844},[623,648],[572,2846],{"className":2847,"style":2537},[833],[572,2849,2107],{"className":2850},[2335],[572,2852],{"className":2853,"style":2537},[833],[572,2855,2857,2860],{"className":2856},[614],[572,2858],{"className":2859,"style":1952},[618],[572,2861,1932],{"className":2862,"style":1956},[623,648],[572,2864,2866,2888],{"className":2865},[575],[572,2867,2869],{"className":2868},[579],[581,2870,2871],{"xmlns":583},[585,2872,2873,2885],{},[588,2874,2875,2877,2879,2881,2883],{},[595,2876,1939],{},[599,2878,765],{},[595,2880,597],{},[599,2882,2723],{},[595,2884,1932],{},[603,2886,2887],{"encoding":605},"v 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v}{2}",[572,2970,2972,2990],{"className":2971,"ariaHidden":593},[610],[572,2973,2975,2978,2981,2984,2987],{"className":2974},[614],[572,2976],{"className":2977,"style":1320},[618],[572,2979,597],{"className":2980},[623,648],[572,2982],{"className":2983,"style":834},[833],[572,2985,765],{"className":2986},[838],[572,2988],{"className":2989,"style":834},[833],[572,2991,2993,2997],{"className":2992},[614],[572,2994],{"className":2995,"style":2996},[618],"height:1.1473em;vertical-align:-0.345em;",[572,2998,3000,3004,3076],{"className":2999},[623],[572,3001],{"className":3002},[855,3003],"nulldelimiter",[572,3005,3007],{"className":3006},[2954],[572,3008,3010,3067],{"className":3009},[628,1095],[572,3011,3013,3064],{"className":3012},[632],[572,3014,3017,3032,3043],{"className":3015,"style":3016},[636],"height:0.8023em;",[572,3018,3020,3023],{"style":3019},"top:-2.655em;",[572,3021],{"className":3022,"style":644},[643],[572,3024,3026],{"className":3025},[1113,1114,1115,1116],[572,3027,3029],{"className":3028},[623,1116],[572,3030,1435],{"className":3031},[623,1116],[572,3033,3035,3038],{"style":3034},"top:-3.23em;",[572,3036],{"className":3037,"style":644},[643],[572,3039],{"className":3040,"style":3042},[3041],"frac-line","border-bottom-width:0.04em;",[572,3044,3046,3049],{"style":3045},"top:-3.394em;",[572,3047],{"className":3048,"style":644},[643],[572,3050,3052],{"className":3051},[1113,1114,1115,1116],[572,3053,3055,3058,3061],{"className":3054},[623,1116],[572,3056,694],{"className":3057},[623,648,1116],[572,3059,2107],{"className":3060},[2335,1116],[572,3062,1939],{"className":3063,"style":1956},[623,648,1116],[572,3065,1124],{"className":3066},[1123],[572,3068,3070],{"className":3069},[632],[572,3071,3074],{"className":3072,"style":3073},[636],"height:0.345em;",[572,3075],{},[572,3077],{"className":3078},[894,3003],[572,3080,3082,3110],{"className":3081},[575],[572,3083,3085],{"className":3084},[579],[581,3086,3087],{"xmlns":583},[585,3088,3089,3107],{},[588,3090,3091,3093,3095],{},[595,3092,1932],{},[599,3094,765],{},[2954,3096,3097,3105],{},[588,3098,3099,3101,3103],{},[595,3100,694],{},[599,3102,2723],{},[595,3104,1939],{},[1433,3106,1435],{},[603,3108,3109],{"encoding":605},"y = \\frac{u - 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also",[572,3213,3215],{"className":3214},[2047],[572,3216,3218,3330],{"className":3217},[575],[572,3219,3221],{"className":3220},[579],[581,3222,3223],{"xmlns":583,"display":2056},[585,3224,3225,3327],{},[588,3226,3227,3233,3235,3299,3302,3305,3307,3309,3311,3317,3319,3321],{},[1046,3228,3229,3231],{},[595,3230,1050],{},[595,3232,769],{"mathvariant":768},[599,3234,765],{},[588,3236,3237,3239,3297],{},[599,3238,773],{"fence":593},[3240,3241,3245,3271],"mtable",{"rowspacing":3242,"columnalign":3243,"columnspacing":3244},"0.16em","center 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= \\begin{pmatrix} \\frac{1}{2} & \\frac{1}{2} \\\\ \\frac{1}{2} & -\\frac{1}{2} \\end{pmatrix}, \\qquad |\\det J_\\Phi| = 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neue Bereich ist das Quadrat ",[572,3943,3945,3975],{"className":3944},[575],[572,3946,3948],{"className":3947},[579],[581,3949,3950],{"xmlns":583},[585,3951,3952,3972],{},[588,3953,3954,3957,3959,3961,3963,3965],{},[599,3955,3956],{"stretchy":772},"[",[599,3958,2723],{},[1433,3960,2076],{},[599,3962,3301],{"separator":593},[1433,3964,2076],{},[1157,3966,3967,3970],{},[599,3968,3969],{"stretchy":772},"]",[1433,3971,1435],{},[603,3973,3974],{"encoding":605},"[-1, 1]^2",[572,3976,3978],{"className":3977,"ariaHidden":593},[610],[572,3979,3981,3984,3987,3990,3993,3996,3999,4002],{"className":3980},[614],[572,3982],{"className":3983,"style":2550},[618],[572,3985,3956],{"className":3986},[855],[572,3988,2723],{"className":3989},[623],[572,3991,2076],{"className":3992},[623],[572,3994,3301],{"className":3995},[3794],[572,3997],{"className":3998,"style":1073},[833],[572,4000,2076],{"className":4001},[623],[572,4003,4005,4008],{"className":4004},[894],[572,4006,3969],{"className":4007},[894],[572,4009,4011],{"className":4010},[1091],[572,4012,4014],{"className":4013},[628],[572,4015,4017],{"className":4016},[632],[572,4018,4020],{"className":4019,"style":1489},[636],[572,4021,4022,4025],{"style":1212},[572,4023],{"className":4024,"style":1109},[643],[572,4026,4028],{"className":4027},[1113,1114,1115,1116],[572,4029,1435],{"className":4030},[623,1116],[572,4032,4034],{"className":4033},[2047],[572,4035,4037,4159],{"className":4036},[575],[572,4038,4040],{"className":4039},[579],[581,4041,4042],{"xmlns":583,"display":2056},[585,4043,4044,4156],{},[588,4045,4046,4052,4054,4056,4058,4060,4066,4068,4070,4072,4074,4088,4100,4106,4109,4115,4117,4119,4121,4123,4125,4127,4129,4135,4137,4144,4146,4148,4150],{},[1046,4047,4048,4050],{},[599,4049,2069],{},[595,4051,2449],{},[599,4053,773],{"stretchy":772},[595,4055,597],{},[599,4057,2107],{},[595,4059,1932],{},[1157,4061,4062,4064],{},[599,4063,782],{"stretchy":772},[1433,4065,1435],{},[2071,4067,2079],{},[595,4069,2082],{},[595,4071,1556],{},[599,4073,765],{},[4075,4076,4077,4080,4086],"msubsup",{},[599,4078,4079],{},"∫",[588,4081,4082,4084],{},[599,4083,2723],{},[1433,4085,2076],{},[1433,4087,2076],{},[4075,4089,4090,4092,4098],{},[599,4091,4079],{},[588,4093,4094,4096],{},[599,4095,2723],{},[1433,4097,2076],{},[1433,4099,2076],{},[1157,4101,4102,4104],{},[595,4103,694],{},[1433,4105,1435],{},[599,4107,4108],{},"⋅",[2954,4110,4111,4113],{},[1433,4112,2076],{},[1433,4114,1435],{},[2071,4116,2079],{},[595,4118,2082],{},[595,4120,694],{},[2071,4122,2079],{},[595,4124,2082],{},[595,4126,1939],{},[599,4128,765],{},[2954,4130,4131,4133],{},[1433,4132,2076],{},[1433,4134,1435],{},[599,4136,4108],{},[2954,4138,4139,4141],{},[1433,4140,1435],{},[1433,4142,4143],{},"3",[599,4145,4108],{},[1433,4147,1435],{},[599,4149,765],{},[2954,4151,4152,4154],{},[1433,4153,1435],{},[1433,4155,4143],{},[603,4157,4158],{"encoding":605},"\\iint_D (x + y)^2\\, dA = \\int_{-1}^1 \\int_{-1}^1 u^2 \\cdot \\frac{1}{2}\\, du\\, dv = \\frac{1}{2} \\cdot \\frac{2}{3} \\cdot 2 = \\frac{2}{3}",[572,4160,4162,4226,4285,4455,4550,4627,4704,4722],{"className":4161,"ariaHidden":593},[610],[572,4163,4165,4169,4211,4214,4217,4220,4223],{"className":4164},[614],[572,4166],{"className":4167,"style":4168},[618],"height:2.2717em;vertical-align:-0.9117em;",[572,4170,4172,4175],{"className":4171},[1077],[572,4173,2069],{"className":4174,"style":2183},[1077,2181,2182],[572,4176,4178],{"className":4177},[1091],[572,4179,4181,4202],{"className":4180},[628,1095],[572,4182,4184,4199],{"className":4183},[632],[572,4185,4188],{"className":4186,"style":4187},[636],"height:-0.4334em;",[572,4189,4190,4193],{"style":2199},[572,4191],{"className":4192,"style":1109},[643],[572,4194,4196],{"className":4195},[1113,1114,1115,1116],[572,4197,2449],{"className":4198,"style":1324},[623,648,1116],[572,4200,1124],{"className":4201},[1123],[572,4203,4205],{"className":4204},[632],[572,4206,4209],{"className":4207,"style":4208},[636],"height:0.9117em;",[572,4210],{},[572,4212,773],{"className":4213},[855],[572,4215,597],{"className":4216},[623,648],[572,4218],{"className":4219,"style":2537},[833],[572,4221,2107],{"className":4222},[2335],[572,4224],{"className":4225,"style":2537},[833],[572,4227,4229,4233,4236,4267,4270,4273,4276,4279,4282],{"className":4228},[614],[572,4230],{"className":4231,"style":4232},[618],"height:1.1141em;vertical-align:-0.25em;",[572,4234,1932],{"className":4235,"style":1956},[623,648],[572,4237,4239,4242],{"className":4238},[894],[572,4240,782],{"className":4241},[894],[572,4243,4245],{"className":4244},[1091],[572,4246,4248],{"className":4247},[628],[572,4249,4251],{"className":4250},[632],[572,4252,4255],{"className":4253,"style":4254},[636],"height:0.8641em;",[572,4256,4258,4261],{"style":4257},"top:-3.113em;margin-right:0.05em;",[572,4259],{"className":4260,"style":1109},[643],[572,4262,4264],{"className":4263},[1113,1114,1115,1116],[572,4265,1435],{"className":4266},[623,1116],[572,4268],{"className":4269,"style":1073},[833],[572,4271,2082],{"className":4272},[623,648],[572,4274,1556],{"className":4275},[623,648],[572,4277],{"className":4278,"style":834},[833],[572,4280,765],{"className":4281},[838],[572,4283],{"className":4284,"style":834},[833],[572,4286,4288,4292,4354,4357,4414,4417,4446,4449,4452],{"className":4287},[614],[572,4289],{"className":4290,"style":4291},[618],"height:2.5343em;vertical-align:-0.9703em;",[572,4293,4295,4299],{"className":4294},[1077],[572,4296,4079],{"className":4297,"style":4298},[1077,2181,2182],"margin-right:0.4445em;position:relative;top:-0.0011em;",[572,4300,4302],{"className":4301},[1091],[572,4303,4305,4345],{"className":4304},[628,1095],[572,4306,4308,4342],{"className":4307},[632],[572,4309,4312,4330],{"className":4310,"style":4311},[636],"height:1.564em;",[572,4313,4315,4318],{"style":4314},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[572,4316],{"className":4317,"style":1109},[643],[572,4319,4321],{"className":4320},[1113,1114,1115,1116],[572,4322,4324,4327],{"className":4323},[623,1116],[572,4325,2723],{"className":4326},[623,1116],[572,4328,2076],{"className":4329},[623,1116],[572,4331,4333,4336],{"style":4332},"top:-3.8129em;margin-right:0.05em;",[572,4334],{"className":4335,"style":1109},[643],[572,4337,4339],{"className":4338},[1113,1114,1115,1116],[572,4340,2076],{"className":4341},[623,1116],[572,4343,1124],{"className":4344},[1123],[572,4346,4348],{"className":4347},[632],[572,4349,4352],{"className":4350,"style":4351},[636],"height:0.9703em;",[572,4353],{},[572,4355],{"className":4356,"style":1073},[833],[572,4358,4360,4363],{"className":4359},[1077],[572,4361,4079],{"className":4362,"style":4298},[1077,2181,2182],[572,4364,4366],{"className":4365},[1091],[572,4367,4369,4406],{"className":4368},[628,1095],[572,4370,4372,4403],{"className":4371},[632],[572,4373,4375,4392],{"className":4374,"style":4311},[636],[572,4376,4377,4380],{"style":4314},[572,4378],{"className":4379,"style":1109},[643],[572,4381,4383],{"className":4382},[1113,1114,1115,1116],[572,4384,4386,4389],{"className":4385},[623,1116],[572,4387,2723],{"className":4388},[623,1116],[572,4390,2076],{"className":4391},[623,1116],[572,4393,4394,4397],{"style":4332},[572,4395],{"className":4396,"style":1109},[643],[572,4398,4400],{"className":4399},[1113,1114,1115,1116],[572,4401,2076],{"className":4402},[623,1116],[572,4404,1124],{"className":4405},[1123],[572,4407,4409],{"className":4408},[632],[572,4410,4412],{"className":4411,"style":4351},[636],[572,4413],{},[572,4415],{"className":4416,"style":1073},[833],[572,4418,4420,4423],{"className":4419},[623],[572,4421,694],{"className":4422},[623,648],[572,4424,4426],{"className":4425},[1091],[572,4427,4429],{"className":4428},[628],[572,4430,4432],{"className":4431},[632],[572,4433,4435],{"className":4434,"style":4254},[636],[572,4436,4437,4440],{"style":4257},[572,4438],{"className":4439,"style":1109},[643],[572,4441,4443],{"className":4442},[1113,1114,1115,1116],[572,4444,1435],{"className":4445},[623,1116],[572,44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assName":4764,"style":3042},[3041],[572,4766,4767,4770],{"style":3914},[572,4768],{"className":4769,"style":644},[643],[572,4771,4773],{"className":4772},[623],[572,4774,1435],{"className":4775},[623],[572,4777,1124],{"className":4778},[1123],[572,4780,4782],{"className":4781},[632],[572,4783,4785],{"className":4784,"style":3933},[636],[572,4786],{},[572,4788],{"className":4789},[894,3003],[559,4791,4793],{"id":4792},"typische-fehler","Typische Fehler",[1242,4795,4796,4978,5552],{},[1245,4797,4798,4799,4977],{},"Den Betrag weglassen. Mit ",[572,4800,4802,4834],{"className":4801},[575],[572,4803,4805],{"className":4804},[579],[581,4806,4807],{"xmlns":583},[585,4808,4809,4831],{},[588,4810,4811,4813,4815,4821,4823,4825],{},[595,4812,1041],{},[599,4814,1044],{},[1046,4816,4817,4819],{},[595,4818,1050],{},[595,4820,769],{"mathvariant":768},[599,4822,765],{},[599,4824,2723],{},[2954,4826,4827,4829],{},[1433,4828,2076],{},[1433,4830,1435],{},[603,4832,4833],{"encoding":605},"\\det J_\\Phi = -\\frac{1}{2}",[572,4835,4837,4899],{"className":4836,"ariaHidden":593},[610],[572,4838,4840,4844,4847,4850,4890,4893,4896],{"className":4839},[614],[572,4841],{"className":4842,"style":4843},[618],"height:0.8444em;vertical-align:-0.15em;",[572,4845,1041],{"className":4846},[1077],[572,4848],{"className":4849,"style":1073},[833],[572,4851,4853,4856],{"className":4852},[623],[572,4854,1050],{"className":4855,"style":1087},[623,648],[572,4857,4859],{"className":4858},[1091],[572,4860,4862,4882],{"className":4861},[628,1095],[572,4863,4865,4879],{"className":4864},[632],[572,4866,4868],{"className":4867,"style":1102},[636],[572,4869,4870,4873],{"style":1105},[572,4871],{"className":4872,"style":1109},[643],[572,4874,4876],{"className":4875},[1113,1114,1115,1116],[572,4877,769],{"className":4878},[623,1116],[572,4880,1124],{"className":4881},[1123],[572,4883,4885],{"className":4884},[632],[572,4886,4888],{"className":4887,"style":1131},[636],[572,4889],{},[572,4891],{"className":4892,"style":834},[833],[572,4894,765],{"className":4895},[838],[572,4897],{"className":4898,"style":834},[833],[572,4900,4902,4906,4909],{"className":4901},[614],[572,4903],{"className":4904,"style":4905},[618],"height:1.1901em;vertical-align:-0.345em;",[572,4907,2723],{"className":4908},[623],[572,4910,4912,4915,4974],{"className":4911},[623],[572,4913],{"className":4914},[855,3003],[572,4916,4918],{"className":4917},[2954],[572,4919,4921,4966],{"className":4920},[628,1095],[572,4922,4924,4963],{"className":4923},[632],[572,4925,4927,4941,4949],{"className":4926,"style":3456},[636],[572,4928,4929,4932],{"style":3019},[572,4930],{"className":4931,"style":644},[643],[572,4933,4935],{"className":4934},[1113,1114,1115,1116],[572,4936,4938],{"className":4937},[623,1116],[572,4939,1435],{"className":4940},[623,1116],[572,4942,4943,4946],{"style":3034},[572,4944],{"className":4945,"style":644},[643],[572,4947],{"className":4948,"style":3042},[3041],[572,4950,4951,4954],{"style":3045},[572,4952],{"className":4953,"style":644},[643],[572,4955,4957],{"className":4956},[1113,1114,1115,1116],[572,4958,4960],{"className":4959},[623,1116],[572,4961,2076],{"className":4962},[623,1116],[572,4964,1124],{"className":4965},[1123],[572,4967,4969],{"className":4968},[632],[572,4970,4972],{"className":4971,"style":3073},[636],[572,4973],{},[572,4975],{"className":4976},[894,3003]," wäre das Ergebnis negativ, obwohl der Integrand nicht negativ ist.",[1245,4979,4980,4981,5079,5080,5115,5116,5240,5241,5344,5345,5551],{},"Die Determinante der falschen Richtung verwenden. Hier hat ",[572,4982,4984,5019],{"className":4983},[575],[572,4985,4987],{"className":4986},[579],[581,4988,4989],{"xmlns":583},[585,4990,4991,5016],{},[588,4992,4993,4995,4997,4999,5001,5003,5006,5008,5010,5012,5014],{},[599,4994,773],{"stretchy":772},[595,4996,597],{},[599,4998,3301],{"separator":593},[595,5000,1932],{},[599,5002,782],{"stretchy":772},[599,5004,5005],{},"↦",[599,5007,773],{"stretchy":772},[595,5009,694],{},[599,5011,3301],{"separator":593},[595,5013,1939],{},[599,5015,782],{"stretchy":772},[603,5017,5018],{"encoding":605},"(x, y) \\mapsto (u, v)",[572,5020,5022,5055],{"className":5021,"ariaHidden":593},[610],[572,5023,5025,5028,5031,5034,5037,5040,5043,5046,5049,5052],{"className":5024},[614],[572,5026],{"className":5027,"style":848},[618],[572,5029,773],{"className":5030},[855],[572,5032,597],{"className":5033},[623,648],[572,5035,3301],{"className":5036},[3794],[572,5038],{"className":5039,"style":1073},[833],[572,5041,1932],{"className":5042,"style":1956},[623,648],[572,5044,782],{"className":5045},[894],[572,5047],{"className":5048,"style":834},[833],[572,5050,5005],{"className":5051},[838],[572,5053],{"className":5054,"style":834},[833],[572,5056,5058,5061,5064,5067,5070,5073,5076],{"className":5057},[614],[572,5059],{"className":5060,"style":848},[618],[572,5062,773],{"className":5063},[855],[572,5065,694],{"className":5066},[623,648],[572,5068,3301],{"className":5069},[3794],[572,5071],{"className":5072,"style":1073},[833],[572,5074,1939],{"className":5075,"style":1956},[623,648],[572,5077,782],{"className":5078},[894]," die Determinante ",[572,5081,5083,5099],{"className":5082},[575],[572,5084,5086],{"className":5085},[579],[581,5087,5088],{"xmlns":583},[585,5089,5090,5096],{},[588,5091,5092,5094],{},[599,5093,2723],{},[1433,5095,1435],{},[603,5097,5098],{"encoding":605},"-2",[572,5100,5102],{"className":5101,"ariaHidden":593},[610],[572,5103,5105,5109,5112],{"className":5104},[614],[572,5106],{"className":5107,"style":5108},[618],"height:0.7278em;vertical-align:-0.0833em;",[572,5110,2723],{"className":5111},[623],[572,5113,1435],{"className":5114},[623],"; gebraucht wird die der Abbildung ",[572,5117,5119,5145],{"className":5118},[575],[572,5120,5122],{"className":5121},[579],[581,5123,5124],{"xmlns":583},[585,5125,5126,5142],{},[588,5127,5128,5134,5136],{},[591,5129,5130,5132],{"accent":593},[595,5131,694],{},[599,5133,601],{},[599,5135,5005],{},[591,5137,5138,5140],{"accent":593},[595,5139,597],{},[599,5141,601],{},[603,5143,5144],{"encoding":605},"\\vec u \\mapsto \\vec x",[572,5146,5148,5199],{"className":5147,"ariaHidden":593},[610],[572,5149,5151,5155,5190,5193,5196],{"className":5150},[614],[572,5152],{"className":5153,"style":5154},[618],"height:0.725em;vertical-align:-0.011em;",[572,5156,5158],{"className":5157},[623,624],[572,5159,5161],{"className":5160},[628],[572,5162,5164],{"className":5163},[632],[572,5165,5167,5175],{"className":5166,"style":619},[636],[572,5168,5169,5172],{"style":639},[572,5170],{"className":5171,"style":644},[643],[572,5173,694],{"className":5174},[623,648],[572,5176,5177,5180],{"style":639},[572,5178],{"className":5179,"style":644},[643],[572,5181,5183],{"className":5182,"style":658},[657],[572,5184,5186],{"className":5185,"style":663},[662],[665,5187,5188],{"xmlns":667,"width":668,"height":669,"style":670,"viewBox":671,"preserveAspectRatio":672},[674,5189],{"d":676},[572,5191],{"className":5192,"style":834},[833],[572,5194,5005],{"className":5195},[838],[572,5197],{"className":5198,"style":834},[833],[572,5200,5202,5205],{"className":5201},[614],[572,5203],{"className":5204,"style":619},[618],[572,5206,5208],{"className":5207},[623,624],[572,5209,5211],{"className":5210},[628],[572,5212,5214],{"className":5213},[632],[572,5215,5217,5225],{"className":5216,"style":619},[636],[572,5218,5219,5222],{"style":639},[572,5220],{"className":5221,"style":644},[643],[572,5223,597],{"className":5224},[623,648],[572,5226,5227,5230],{"style":639},[572,5228],{"className":5229,"style":644},[643],[572,5231,5233],{"className":5232,"style":658},[657],[572,5234,5236],{"className":5235,"style":663},[662],[665,5237,5238],{"xmlns":667,"width":668,"height":669,"style":670,"viewBox":671,"preserveAspectRatio":672},[674,5239],{"d":676},", also ",[572,5242,5244,5264],{"className":5243},[575],[572,5245,5247],{"className":5246},[579],[581,5248,5249],{"xmlns":583},[585,5250,5251,5261],{},[588,5252,5253,5255],{},[599,5254,2723],{},[2954,5256,5257,5259],{},[1433,5258,2076],{},[1433,5260,1435],{},[603,5262,5263],{"encoding":605},"-\\frac{1}{2}",[572,5265,5267],{"className":5266,"ariaHidden":593},[610],[572,5268,5270,5273,5276],{"className":5269},[614],[572,5271],{"className":5272,"style":4905},[618],[572,5274,2723],{"className":5275},[623],[572,5277,5279,5282,5341],{"className":5278},[623],[572,5280],{"className":5281},[855,3003],[572,5283,5285],{"className":5284},[2954],[572,5286,5288,5333],{"className":5287},[628,1095],[572,5289,5291,5330],{"className":5290},[632],[572,5292,5294,5308,5316],{"className":5293,"style":3456},[636],[572,5295,5296,5299],{"style":3019},[572,5297],{"className":5298,"style":644},[643],[572,5300,5302],{"className":5301},[1113,1114,1115,1116],[572,5303,5305],{"className":5304},[623,1116],[572,5306,1435],{"className":5307},[623,1116],[572,5309,5310,5313],{"style":3034},[572,5311],{"className":5312,"style":644},[643],[572,5314],{"className":5315,"style":3042},[3041],[572,5317,5318,5321],{"style":3045},[572,5319],{"className":5320,"style":644},[643],[572,5322,5324],{"className":5323},[1113,1114,1115,1116],[572,5325,5327],{"className":5326},[623,1116],[572,5328,2076],{"className":5329},[623,1116],[572,5331,1124],{"className":5332},[1123],[572,5334,5336],{"className":5335},[632],[572,5337,5339],{"className":5338,"style":3073},[636],[572,5340],{},[572,5342],{"className":5343},[894,3003],". Die Kehrwerte hängen zusammen: ",[572,5346,5348,5382],{"className":5347},[575],[572,5349,5351],{"className":5350},[579],[581,5352,5353],{"xmlns":583},[585,5354,5355,5379],{},[588,5356,5357,5371,5373],{},[2954,5358,5359,5361],{},[1433,5360,2076],{},[588,5362,5363,5365,5367,5369],{},[595,5364,1038],{"mathvariant":768},[599,5366,2723],{},[1433,5368,1435],{},[595,5370,1038],{"mathvariant":768},[599,5372,765],{},[2954,5374,5375,5377],{},[1433,5376,2076],{},[1433,5378,1435],{},[603,5380,5381],{"encoding":605},"\\frac{1}{|-2|} = \\frac{1}{2}",[572,5383,5385,5477],{"className":5384,"ariaHidden":593},[610],[572,5386,5388,5392,5468,5471,5474],{"className":5387},[614],[572,5389],{"className":5390,"style":5391},[618],"height:1.3651em;vertical-align:-0.52em;",[572,5393,5395,5398,5465],{"className":5394},[623],[572,5396],{"className":5397},[855,3003],[572,5399,5401],{"className":5400},[2954],[572,5402,5404,5456],{"className":5403},[628,1095],[572,5405,5407,5453],{"className":5406},[632],[572,5408,5410,5431,5439],{"className":5409,"style":3456},[636],[572,5411,5412,5415],{"style":3019},[572,5413],{"className":5414,"style":644},[643],[572,5416,5418],{"className":5417},[1113,1114,1115,1116],[572,5419,5421,5424,5427],{"className":5420},[623,1116],[572,5422,1038],{"className":5423},[623,1116],[572,5425,2723],{"className":5426},[2335,1116],[572,5428,5430],{"className":5429},[623,1116],"2∣",[572,5432,5433,5436],{"style":3034},[572,5434],{"className":5435,"style":644},[643],[572,5437],{"className":5438,"style":3042},[3041],[572,5440,5441,5444],{"style":3045},[572,5442],{"className":5443,"style":644},[643],[572,5445,5447],{"className":5446},[1113,1114,1115,1116],[572,5448,5450],{"className":5449},[623,1116],[572,5451,2076],{"className":5452},[623,1116],[572,5454,1124],{"className":5455},[1123],[572,5457,5459],{"className":5458},[632],[572,5460,5463],{"className":5461,"style":5462},[636],"height:0.52em;",[572,5464],{},[572,5466],{"className":5467},[894,3003],[572,5469],{"className":5470,"style":834},[833],[572,5472,765],{"className":5473},[838],[572,5475],{"className":5476,"style":834},[833],[572,5478,5480,5483],{"className":5479},[614],[572,5481],{"className":5482,"style":4905},[618],[572,5484,5486,5489,5548],{"className":5485},[623],[572,5487],{"className":5488},[855,3003],[572,5490,5492],{"className":5491},[2954],[572,5493,5495,5540],{"className":5494},[628,1095],[572,5496,5498,5537],{"className":5497},[632],[572,5499,5501,5515,5523],{"className":5500,"style":3456},[636],[572,5502,5503,5506],{"style":3019},[572,5504],{"className":5505,"style":644},[643],[572,5507,5509],{"className":5508},[1113,1114,1115,1116],[572,5510,5512],{"className":5511},[623,1116],[572,5513,1435],{"className":5514},[623,1116],[572,5516,5517,5520],{"style":3034},[572,5518],{"className":5519,"style":644},[643],[572,5521],{"className":5522,"style":3042},[3041],[572,5524,5525,5528],{"style":3045},[572,5526],{"className":5527,"style":644},[643],[572,5529,5531],{"className":5530},[1113,1114,1115,1116],[572,5532,5534],{"className":5533},[623,1116],[572,5535,2076],{"className":5536},[623,1116],[572,5538,1124],{"className":5539},[1123],[572,5541,5543],{"className":5542},[632],[572,5544,5546],{"className":5545,"style":3073},[636],[572,5547],{},[572,5549],{"className":5550},[894,3003],".",[1245,5553,5554],{},"Den Integranden umrechnen, die Grenzen aber nicht. Der Bereich muss vollständig in den neuen Koordinaten beschrieben werden.",{"title":5556,"searchDepth":5557,"depth":5557,"links":5558},"",2,[5559,5560,5561],{"id":561,"depth":5557,"text":562},{"id":1795,"depth":5557,"text":1796},{"id":4792,"depth":5557,"text":4793},[5563,5566,5569,5572,5574,5577,5580],{"lhs":5564,"rhs":5565},"det([[a, 0], [0, b]])","a*b",{"lhs":5567,"rhs":5568},"abs(det([[1\u002F2, 1\u002F2], [1\u002F2, -1\u002F2]]))","1\u002F2",{"lhs":5570,"rhs":5571},"det([[1\u002F2, 1\u002F2], [1\u002F2, -1\u002F2]])","-1\u002F2",{"lhs":5573,"rhs":5098},"det([[1, 1], [1, -1]])",{"lhs":5575,"rhs":5576},"round(sum(map(0:999, f(k) = (-1 + (k + 0.5)*2\u002F1000)^2)) * 2\u002F1000, 4)","round(2\u002F3, 4)",{"lhs":5578,"rhs":5579},"1\u002F2 * 2\u002F3 * 2","2\u002F3",{"lhs":5581,"rhs":5568},"1 \u002F abs(-2)","U \\subseteq \\mathbb{R}^n \\text{ offen},\\ \\Phi\\colon U \\to \\Phi(U) \\text{ bijektiv, stetig differenzierbar},\\ \\det J_\\Phi \\neq 0 \\text{ auf } U,\\ f \\text{ integrierbar über } \\Phi(U)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>U\u003C\u002Fmi>\u003Cmo>⊆\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">U \\subseteq \\mathbb{R}^n\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:0.8193em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">U\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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6644em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">offen\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\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:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">Φ\u003C\u002Fmi>\u003Cmspace>\u003C\u002Fmspace>\u003Cmspace width=\"0.1111em\"\u002F>\u003Cmo lspace=\"0em\" rspace=\"0.17em\">\u003C\u002Fmo>\u003Cmtext> ⁣\u003C\u002Fmtext>\u003Cmo lspace=\"0em\" rspace=\"0em\">:\u003C\u002Fmo>\u003Cmspace width=\"0.3333em\"\u002F>\u003Cmi>U\u003C\u002Fmi>\u003Cmo>→\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">Φ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>U\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\Phi\\colon U \\to \\Phi(U)\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\">Φ\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1111em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:-0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">:\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.3333em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">U\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">Φ\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">U\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">bijektiv, stetig\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">differenzierbar\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\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:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>det\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmsub>\u003Cmi>J\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">Φ\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\det J_\\Phi \\neq 0\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=\"mop\">det\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0962em;\">J\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0962em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">Φ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">auf\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>U\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">U,\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:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">U\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>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\">integrierbar über\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">Φ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>U\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\Phi(U)\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">Φ\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">U\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","change-of-variables","\\int_{\\Phi(U)} f(\\vec{x})\\, d\\vec{x} = \\int_U f\\big(\\Phi(\\vec{u})\\big)\\, \\big|\\det J_\\Phi(\\vec{u})\\big|\\, d\\vec{u}","\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>\u003Cmsub>\u003Cmo>∫\u003C\u002Fmo>\u003Cmrow>\u003Cmi mathvariant=\"normal\">Φ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>U\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmo>∫\u003C\u002Fmo>\u003Cmi>U\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmi>f\u003C\u002Fmi>\u003Cmo fence=\"false\" stretchy=\"true\" minsize=\"1.2em\" maxsize=\"1.2em\">(\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">Φ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo fence=\"false\" stretchy=\"true\" minsize=\"1.2em\" maxsize=\"1.2em\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmo fence=\"false\" stretchy=\"true\" minsize=\"1.2em\" maxsize=\"1.2em\">∣\u003C\u002Fmo>\u003Cmi>det\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmsub>\u003Cmi>J\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">Φ\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo fence=\"false\" stretchy=\"true\" minsize=\"1.2em\" maxsize=\"1.2em\">∣\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\int_{\\Phi(U)} f(\\vec{x})\\, d\\vec{x} = \\int_U f\\big(\\Phi(\\vec{u})\\big)\\, \\big|\\det J_\\Phi(\\vec{u})\\big|\\, d\\vec{u}\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:2.447em;vertical-align:-1.0869em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:-0.3869em;\">\u003Cspan style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">Φ\u003C\u002Fspan>\u003Cspan class=\"mopen mtight\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.109em;\">U\u003C\u002Fspan>\u003Cspan class=\"mclose mtight\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.0869em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.2719em;vertical-align:-0.9119em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t 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