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und integriert über ",[580,1116,1118,1131],{"className":1117},[583],[580,1119,1121],{"className":1120},[587],[589,1122,1123],{"xmlns":591},[593,1124,1125,1129],{},[596,1126,1127],{},[603,1128,785],{},[611,1130,785],{"encoding":613},[580,1132,1134],{"className":1133,"ariaHidden":601},[618],[580,1135,1137,1141],{"className":1136},[622],[580,1138],{"className":1139,"style":1140},[626],"height:0.6151em;",[580,1142,785],{"className":1143},[631,656],". Das Ergebnis hängt nicht von der Wahl der Parametrisierung ab, wohl aber von der Richtung: Rückwärts durchlaufen ändert das Vorzeichen.",[565,1146,1147,1148,1249,1250,1253,1254,1282],{},"Ist ",[580,1149,1151,1179],{"className":1150},[583],[580,1152,1154],{"className":1153},[587],[589,1155,1156],{"xmlns":591},[593,1157,1158,1176],{},[596,1159,1160,1166,1169,1173],{},[599,1161,1162,1164],{"accent":601},[603,1163,605],{},[607,1165,609],{},[607,1167,1168],{},"=",[603,1170,1172],{"mathvariant":1171},"normal","∇",[603,1174,1175],{},"f",[611,1177,1178],{"encoding":613},"\\vec F = \\nabla f",[580,1180,1182,1235],{"className":1181,"ariaHidden":601},[618],[580,1183,1185,1188,1223,1228,1232],{"className":1184},[622],[580,1186],{"className":1187,"style":627},[626],[580,1189,1191],{"className":1190},[631,632],[580,1192,1194],{"className":1193},[636],[580,1195,1197],{"className":1196},[640],[580,1198,1200,1208],{"className":1199,"style":627},[644],[580,1201,1202,1205],{"style":647},[580,1203],{"className":1204,"style":652},[651],[580,1206,605],{"className":1207,"style":657},[631,656],[580,1209,1210,1213],{"style":660},[580,1211],{"className":1212,"style":652},[651],[580,1214,1216],{"className":1215,"style":668},[667],[580,1217,1219],{"className":1218,"style":673},[672],[675,1220,1221],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,1222],{"d":686},[580,1224],{"className":1225,"style":1227},[1226],"mspace","margin-right:0.2778em;",[580,1229,1168],{"className":1230},[1231],"mrel",[580,1233],{"className":1234,"style":1227},[1226],[580,1236,1238,1242,1245],{"className":1237},[622],[580,1239],{"className":1240,"style":1241},[626],"height:0.8889em;vertical-align:-0.1944em;",[580,1243,1172],{"className":1244},[631],[580,1246,1175],{"className":1247,"style":1248},[631,656],"margin-right:0.1076em;"," ein ",[569,1251,1252],{},"Gradientenfeld"," mit stetig differenzierbarem Potential ",[580,1255,1257,1270],{"className":1256},[583],[580,1258,1260],{"className":1259},[587],[589,1261,1262],{"xmlns":591},[593,1263,1264,1268],{},[596,1265,1266],{},[603,1267,1175],{},[611,1269,1175],{"encoding":613},[580,1271,1273],{"className":1272,"ariaHidden":601},[618],[580,1274,1276,1279],{"className":1275},[622],[580,1277],{"className":1278,"style":1241},[626],[580,1280,1175],{"className":1281,"style":1248},[631,656],", hängt das Integral nur vom Anfangs- und Endpunkt ab:",[580,1284,1287],{"className":1285},[1286],"katex-display",[580,1288,1290,1372],{"className":1289},[583],[580,1291,1293],{"className":1292},[587],[589,1294,1296],{"xmlns":591,"display":1295},"block",[593,1297,1298,1369],{},[596,1299,1300,1309,1311,1313,1316,1319,1325,1327,1329,1332,1338,1340,1343,1345,1347,1350,1352,1354,1360,1362,1365,1367],{},[1301,1302,1303,1306],"msub",{},[607,1304,1305],{},"∫",[603,1307,1308],{},"C",[603,1310,1172],{"mathvariant":1171},[603,1312,1175],{},[607,1314,1315],{},"⋅",[603,1317,1318],{},"d",[599,1320,1321,1323],{"accent":601},[603,1322,776],{},[607,1324,609],{},[607,1326,1168],{},[603,1328,1175],{},[607,1330,782],{"fence":781,"stretchy":601,"minsize":1331,"maxsize":1331},"1.2em",[599,1333,1334,1336],{"accent":601},[603,1335,776],{},[607,1337,609],{},[607,1339,782],{"stretchy":781},[603,1341,1342],{},"b",[607,1344,788],{"stretchy":781},[607,1346,788],{"fence":781,"stretchy":601,"minsize":1331,"maxsize":1331},[607,1348,1349],{},"−",[603,1351,1175],{},[607,1353,782],{"fence":781,"stretchy":601,"minsize":1331,"maxsize":1331},[599,1355,1356,1358],{"accent":601},[603,1357,776],{},[607,1359,609],{},[607,1361,782],{"stretchy":781},[603,1363,1364],{},"a",[607,1366,788],{"stretchy":781},[607,1368,788],{"fence":781,"stretchy":601,"minsize":1331,"maxsize":1331},[611,1370,1371],{"encoding":613},"\\int_C \\nabla f \\cdot d\\vec r = f\\big(\\vec r(b)\\big) - f\\big(\\vec r(a)\\big)",[580,1373,1375,1460,1513,1590],{"className":1374,"ariaHidden":601},[618],[580,1376,1378,1382,1439,1443,1446,1449,1453,1457],{"className":1377},[622],[580,1379],{"className":1380,"style":1381},[626],"height:2.2719em;vertical-align:-0.9119em;",[580,1383,1386,1392],{"className":1384},[1385],"mop",[580,1387,1305],{"className":1388,"style":1391},[1385,1389,1390],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[580,1393,1396],{"className":1394},[1395],"msupsub",[580,1397,1400,1430],{"className":1398},[636,1399],"vlist-t2",[580,1401,1403,1425],{"className":1402},[640],[580,1404,1407],{"className":1405,"style":1406},[644],"height:-0.4336em;",[580,1408,1410,1414],{"style":1409},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[580,1411],{"className":1412,"style":1413},[651],"height:2.7em;",[580,1415,1421],{"className":1416},[1417,1418,1419,1420],"sizing","reset-size6","size3","mtight",[580,1422,1308],{"className":1423,"style":1424},[631,656,1420],"margin-right:0.0715em;",[580,1426,1429],{"className":1427},[1428],"vlist-s","​",[580,1431,1433],{"className":1432},[640],[580,1434,1437],{"className":1435,"style":1436},[644],"height:0.9119em;",[580,1438],{},[580,1440],{"className":1441,"style":1442},[1226],"margin-right:0.1667em;",[580,1444,1172],{"className":1445},[631],[580,1447,1175],{"className":1448,"style":1248},[631,656],[580,1450],{"className":1451,"style":1452},[1226],"margin-right:0.2222em;",[580,1454,1315],{"className":1455},[1456],"mbin",[580,1458],{"className":1459,"style":1452},[1226],[580,1461,1463,1466,1469,1504,1507,1510],{"className":1462},[622],[580,1464],{"className":1465,"style":814},[626],[580,1467,1318],{"className":1468},[631,656],[580,1470,1472],{"className":1471},[631,632],[580,1473,1475],{"className":1474},[636],[580,1476,1478],{"className":1477},[640],[580,1479,1481,1489],{"className":1480,"style":814},[644],[580,1482,1483,1486],{"style":647},[580,1484],{"className":1485,"style":652},[651],[580,1487,776],{"className":1488,"style":823},[631,656],[580,1490,1491,1494],{"style":647},[580,1492],{"className":1493,"style":652},[651],[580,1495,1497],{"className":1496,"style":832},[667],[580,1498,1500],{"className":1499,"style":673},[672],[675,1501,1502],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,1503],{"d":686},[580,1505],{"className":1506,"style":1227},[1226],[580,1508,1168],{"className":1509},[1231],[580,1511],{"className":1512,"style":1227},[1226],[580,1514,1516,1520,1523,1531,1566,1569,1572,1575,1581,1584,1587],{"className":1515},[622],[580,1517],{"className":1518,"style":1519},[626],"height:1.2em;vertical-align:-0.35em;",[580,1521,1175],{"className":1522,"style":1248},[631,656],[580,1524,1526],{"className":1525},[631],[580,1527,782],{"className":1528},[1529,1530],"delimsizing","size1",[580,1532,1534],{"className":1533},[631,632],[580,1535,1537],{"className":1536},[636],[580,1538,1540],{"className":1539},[640],[580,1541,1543,1551],{"className":1542,"style":814},[644],[580,1544,1545,1548],{"style":647},[580,1546],{"className":1547,"style":652},[651],[580,1549,776],{"className":1550,"style":823},[631,656],[580,1552,1553,1556],{"style":647},[580,1554],{"className":1555,"style":652},[651],[580,1557,1559],{"className":1558,"style":832},[667],[580,1560,1562],{"className":1561,"style":673},[672],[675,1563,1564],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,1565],{"d":686},[580,1567,782],{"className":1568},[843],[580,1570,1342],{"className":1571},[631,656],[580,1573,788],{"className":1574},[850],[580,1576,1578],{"className":1577},[631],[580,1579,788],{"className":1580},[1529,1530],[580,1582],{"className":1583,"style":1452},[1226],[580,1585,1349],{"className":1586},[1456],[580,1588],{"className":1589,"style":1452},[1226],[580,1591,1593,1596,1599,1605,1640,1643,1646,1649],{"className":1592},[622],[580,1594],{"className":1595,"style":1519},[626],[580,1597,1175],{"className":1598,"style":1248},[631,656],[580,1600,1602],{"className":1601},[631],[580,1603,782],{"className":1604},[1529,1530],[580,1606,1608],{"className":1607},[631,632],[580,1609,1611],{"className":1610},[636],[580,1612,1614],{"className":1613},[640],[580,1615,1617,1625],{"className":1616,"style":814},[644],[580,1618,1619,1622],{"style":647},[580,1620],{"className":1621,"style":652},[651],[580,1623,776],{"className":1624,"style":823},[631,656],[580,1626,1627,1630],{"style":647},[580,1628],{"className":1629,"style":652},[651],[580,1631,1633],{"className":1632,"style":832},[667],[580,1634,1636],{"className":1635,"style":673},[672],[675,1637,1638],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,1639],{"d":686},[580,1641,782],{"className":1642},[843],[580,1644,1364],{"className":1645},[631,656],[580,1647,788],{"className":1648},[850],[580,1650,1652],{"className":1651},[631],[580,1653,788],{"className":1654},[1529,1530],[565,1656,1657,1658,1661,1662,2045,2046,2101],{},"Insbesondere ist das Integral über jede geschlossene Kurve dann null. Davon zu unterscheiden ist das ",[569,1659,1660],{},"skalare Kurvenintegral"," ",[580,1663,1665,1753],{"className":1664},[583],[580,1666,1668],{"className":1667},[587],[589,1669,1670],{"xmlns":591},[593,1671,1672,1750],{},[596,1673,1674,1680,1683,1687,1689,1692,1694,1703,1705,1707,1713,1715,1717,1719,1721,1723,1726,1736,1738,1740,1742,1744,1746,1748],{},[1301,1675,1676,1678],{},[607,1677,1305],{},[603,1679,1308],{},[603,1681,1682],{},"g",[1684,1685,1686],"mtext",{}," ",[603,1688,1318],{},[603,1690,1691],{},"s",[607,1693,1168],{},[1695,1696,1697,1699,1701],"msubsup",{},[607,1698,1305],{},[603,1700,1364],{},[603,1702,1342],{},[603,1704,1682],{},[607,1706,782],{"fence":781,"stretchy":601,"minsize":1331,"maxsize":1331},[599,1708,1709,1711],{"accent":601},[603,1710,776],{},[607,1712,609],{},[607,1714,782],{"stretchy":781},[603,1716,785],{},[607,1718,788],{"stretchy":781},[607,1720,788],{"fence":781,"stretchy":601,"minsize":1331,"maxsize":1331},[1684,1722,1686],{},[603,1724,1725],{"mathvariant":1171},"∣",[599,1727,1728,1734],{"accent":601},[599,1729,1730,1732],{"accent":601},[603,1731,776],{},[607,1733,609],{},[607,1735,1019],{},[607,1737,782],{"stretchy":781},[603,1739,785],{},[607,1741,788],{"stretchy":781},[603,1743,1725],{"mathvariant":1171},[1684,1745,1686],{},[603,1747,1318],{},[603,1749,785],{},[611,1751,1752],{"encoding":613},"\\int_C g\\, ds = \\int_a^b g\\big(\\vec r(t)\\big)\\, |\\dot{\\vec r}(t)|\\, dt",[580,1754,1756,1833],{"className":1755,"ariaHidden":601},[618],[580,1757,1759,1763,1808,1811,1815,1818,1821,1824,1827,1830],{"className":1758},[622],[580,1760],{"className":1761,"style":1762},[626],"height:1.1608em;vertical-align:-0.3558em;",[580,1764,1766,1771],{"className":1765},[1385],[580,1767,1305],{"className":1768,"style":1770},[1385,1389,1769],"small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[580,1772,1774],{"className":1773},[1395],[580,1775,1777,1799],{"className":1776},[636,1399],[580,1778,1780,1796],{"className":1779},[640],[580,1781,1784],{"className":1782,"style":1783},[644],"height:0.1225em;",[580,1785,1787,1790],{"style":1786},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[580,1788],{"className":1789,"style":1413},[651],[580,1791,1793],{"className":1792},[1417,1418,1419,1420],[580,1794,1308],{"className":1795,"style":1424},[631,656,1420],[580,1797,1429],{"className":1798},[1428],[580,1800,1802],{"className":1801},[640],[580,1803,1806],{"className":1804,"style":1805},[644],"height:0.3558em;",[580,1807],{},[580,1809],{"className":1810,"style":1442},[1226],[580,1812,1682],{"className":1813,"style":1814},[631,656],"margin-right:0.0359em;",[580,1816],{"className":1817,"style":1442},[1226],[580,1819,1318],{"className":1820},[631,656],[580,1822,1691],{"className":1823},[631,656],[580,1825],{"className":1826,"style":1227},[1226],[580,1828,1168],{"className":1829},[1231],[580,1831],{"className":1832,"style":1227},[1226],[580,1834,1836,1840,1893,1896,1899,1905,1940,1943,1946,1949,1955,1958,1961,2024,2027,2030,2033,2036,2039,2042],{"className":1835},[622],[580,1837],{"className":1838,"style":1839},[626],"height:1.3998em;vertical-align:-0.3558em;",[580,1841,1843,1846],{"className":1842},[1385],[580,1844,1305],{"className":1845,"style":1770},[1385,1389,1769],[580,1847,1849],{"className":1848},[1395],[580,1850,1852,1885],{"className":1851},[636,1399],[580,1853,1855,1882],{"className":1854},[640],[580,1856,1859,1870],{"className":1857,"style":1858},[644],"height:1.044em;",[580,1860,1861,1864],{"style":1786},[580,1862],{"className":1863,"style":1413},[651],[580,1865,1867],{"className":1866},[1417,1418,1419,1420],[580,1868,1364],{"className":1869},[631,656,1420],[580,1871,1873,1876],{"style":1872},"top:-3.2579em;margin-right:0.05em;",[580,1874],{"className":1875,"style":1413},[651],[580,1877,1879],{"className":1878},[1417,1418,1419,1420],[580,1880,1342],{"className":1881},[631,656,1420],[580,1883,1429],{"className":1884},[1428],[580,1886,1888],{"className":1887},[640],[580,1889,1891],{"className":1890,"style":1805},[644],[580,1892],{},[580,1894],{"className":1895,"style":1442},[1226],[580,1897,1682],{"className":1898,"style":1814},[631,656],[580,1900,1902],{"className":1901},[631],[580,1903,782],{"className":1904},[1529,1530],[580,1906,1908],{"className":1907},[631,632],[580,1909,1911],{"className":1910},[636],[580,1912,1914],{"className":1913},[640],[580,1915,1917,1925],{"className":1916,"style":814},[644],[580,1918,1919,1922],{"style":647},[580,1920],{"className":1921,"style":652},[651],[580,1923,776],{"className":1924,"style":823},[631,656],[580,1926,1927,1930],{"style":647},[580,1928],{"className":1929,"style":652},[651],[580,1931,1933],{"className":1932,"style":832},[667],[580,1934,1936],{"className":1935,"style":673},[672],[675,1937,1938],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,1939],{"d":686},[580,1941,782],{"className":1942},[843],[580,1944,785],{"className":1945},[631,656],[580,1947,788],{"className":1948},[850],[580,1950,1952],{"className":1951},[631],[580,1953,788],{"className":1954},[1529,1530],[580,1956],{"className":1957,"style":1442},[1226],[580,1959,1725],{"className":1960},[631],[580,1962,1964],{"className":1963},[631,632],[580,1965,1967],{"className":1966},[636],[580,1968,1970],{"className":1969},[640],[580,1971,1973,2013],{"className":1972,"style":1051},[644],[580,1974,1975,1978],{"style":647},[580,1976],{"className":1977,"style":652},[651],[580,1979,1981],{"className":1980},[631,632],[580,1982,1984],{"className":1983},[636],[580,1985,1987],{"className":1986},[640],[580,1988,1990,1998],{"className":1989,"style":814},[644],[580,1991,1992,1995],{"style":647},[580,1993],{"className":1994,"style":652},[651],[580,1996,776],{"className":1997,"style":823},[631,656],[580,1999,2000,2003],{"style":647},[580,2001],{"className":2002,"style":652},[651],[580,2004,2006],{"className":2005,"style":832},[667],[580,2007,2009],{"className":2008,"style":673},[672],[675,2010,2011],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,2012],{"d":686},[580,2014,2015,2018],{"style":1094},[580,2016],{"className":2017,"style":652},[651],[580,2019,2021],{"className":2020,"style":1101},[667],[580,2022,1019],{"className":2023},[631],[580,2025,782],{"className":2026},[843],[580,2028,785],{"className":2029},[631,656],[580,2031,788],{"className":2032},[850],[580,2034,1725],{"className":2035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z.B. für die Masse eines Drahts. Mit ",[580,2047,2049,2069],{"className":2048},[583],[580,2050,2052],{"className":2051},[587],[589,2053,2054],{"xmlns":591},[593,2055,2056,2066],{},[596,2057,2058,2060,2062],{},[603,2059,1682],{},[607,2061,1168],{},[2063,2064,2065],"mn",{},"1",[611,2067,2068],{"encoding":613},"g = 1",[580,2070,2072,2091],{"className":2071,"ariaHidden":601},[618],[580,2073,2075,2079,2082,2085,2088],{"className":2074},[622],[580,2076],{"className":2077,"style":2078},[626],"height:0.625em;vertical-align:-0.1944em;",[580,2080,1682],{"className":2081,"style":1814},[631,656],[580,2083],{"className":2084,"style":1227},[1226],[580,2086,1168],{"className":2087},[1231],[580,2089],{"className":2090,"style":1227},[1226],[580,2092,2094,2098],{"className":2093},[622],[580,2095],{"className":2096,"style":2097},[626],"height:0.6444em;",[580,2099,2065],{"className":2100},[631]," liefert es die Bogenlänge.",[560,2103,2105],{"id":2104},"beispiele","Beispiele",[565,2107,2108,2109,2298,2299,2482,2483,2567],{},"Für 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längs des Einheitskreises ",[580,2300,2302,2355],{"className":2301},[583],[580,2303,2305],{"className":2304},[587],[589,2306,2307],{"xmlns":591},[593,2308,2309,2352],{},[596,2310,2311,2317,2319,2321,2323,2325,2327,2330,2333,2335,2337,2339,2342,2344,2346],{},[599,2312,2313,2315],{"accent":601},[603,2314,776],{},[607,2316,609],{},[607,2318,782],{"stretchy":781},[603,2320,785],{},[607,2322,788],{"stretchy":781},[607,2324,1168],{},[607,2326,782],{"stretchy":781},[603,2328,2329],{},"cos",[607,2331,2332],{},"⁡",[603,2334,785],{},[607,2336,2134],{"separator":601},[1684,2338,2152],{},[603,2340,2341],{},"sin",[607,2343,2332],{},[603,2345,785],{},[2156,2347,2348,2350],{},[607,2349,788],{"stretchy":781},[603,2351,2162],{},[611,2353,2354],{"encoding":613},"\\vec r(t) = (\\cos t,\\ \\sin 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",[580,2484,2486,2514],{"className":2485},[583],[580,2487,2489],{"className":2488},[587],[589,2490,2491],{"xmlns":591},[593,2492,2493,2511],{},[596,2494,2495,2498,2501,2503,2505,2508],{},[2063,2496,2497],{},"0",[607,2499,2500],{},"≤",[603,2502,785],{},[607,2504,2500],{},[2063,2506,2507],{},"2",[603,2509,2510],{},"π",[611,2512,2513],{"encoding":613},"0 \\leq t \\leq 2\\pi",[580,2515,2517,2536,2555],{"className":2516,"ariaHidden":601},[618],[580,2518,2520,2524,2527,2530,2533],{"className":2519},[622],[580,2521],{"className":2522,"style":2523},[626],"height:0.7804em;vertical-align:-0.136em;",[580,2525,2497],{"className":2526},[631],[580,2528],{"className":2529,"style":1227},[1226],[580,2531,2500],{"className":2532},[1231],[580,2534],{"className":2535,"style":1227},[1226],[580,2537,2539,2543,2546,2549,2552],{"className":2538},[622],[580,2540],{"className":2541,"style":2542},[626],"height:0.7719em;vertical-align:-0.136em;",[580,2544,785],{"className":2545},[631,656],[580,2547],{"className":2548,"style":1227},[1226],[580,2550,2500],{"className":2551},[1231],[580,2553],{"className":2554,"style":1227},[1226],[580,2556,2558,2561,2564],{"className":2557},[622],[580,2559],{"className":2560,"style":2097},[626],[580,2562,2507],{"className":2563},[631],[580,2565,2510],{"className":2566,"style":1814},[631,656],", gegen den Uhrzeigersinn:",[580,2569,2571],{"className":2570},[1286],[580,2572,2574,2740],{"className":2573},[583],[580,2575,2577],{"className":2576},[587],[589,2578,2579],{"xmlns":591,"display":1295},[593,2580,2581,2737],{},[596,2582,2583,2590,2596,2598,2600,2606,2608,2620,2665,2667,2705,2707,2709,2711,2723,2725,2727,2729,2731,2733,2735],{},[1301,2584,2585,2588],{},[607,2586,2587],{},"∮",[603,2589,1308],{},[599,2591,2592,2594],{"accent":601},[603,2593,605],{},[607,2595,609],{},[607,2597,1315],{},[603,2599,1318],{},[599,2601,2602,2604],{"accent":601},[603,2603,776],{},[607,2605,609],{},[607,2607,1168],{},[1695,2609,2610,2612,2614],{},[607,2611,1305],{},[2063,2613,2497],{},[596,2615,2616,2618],{},[2063,2617,2507],{},[603,2619,2510],{},[596,2621,2622,2624,2663],{},[607,2623,782],{"fence":601},[2625,2626,2630,2649],"mtable",{"rowspacing":2627,"columnalign":2628,"columnspacing":2629},"0.16em","center","1em",[2631,2632,2633],"mtr",{},[2634,2635,2636],"mtd",{},[2637,2638,2639],"mstyle",{"scriptlevel":2497,"displaystyle":781},[596,2640,2641,2643,2645,2647],{},[607,2642,1349],{},[603,2644,2341],{},[607,2646,2332],{},[603,2648,785],{},[2631,2650,2651],{},[2634,2652,2653],{},[2637,2654,2655],{"scriptlevel":2497,"displaystyle":781},[596,2656,2657,2659,2661],{},[603,2658,2329],{},[607,2660,2332],{},[603,2662,785],{},[607,2664,788],{"fence":601},[607,2666,1315],{},[596,2668,2669,2671,2703],{},[607,2670,782],{"fence":601},[2625,2672,2673,2689],{"rowspacing":2627,"columnalign":2628,"columnspacing":2629},[2631,2674,2675],{},[2634,2676,2677],{},[2637,2678,2679],{"scriptlevel":2497,"displaystyle":781},[596,2680,2681,2683,2685,2687],{},[607,2682,1349],{},[603,2684,2341],{},[607,2686,2332],{},[603,2688,785],{},[2631,2690,2691],{},[2634,2692,2693],{},[2637,2694,2695],{"scriptlevel":2497,"displaystyle":781},[596,2696,2697,2699,2701],{},[603,2698,2329],{},[607,2700,2332],{},[603,2702,785],{},[607,2704,788],{"fence":601},[603,2706,1318],{},[603,2708,785],{},[607,2710,1168],{},[1695,2712,2713,2715,2717],{},[607,2714,1305],{},[2063,2716,2497],{},[596,2718,2719,2721],{},[2063,2720,2507],{},[603,2722,2510],{},[2063,2724,2065],{},[1684,2726,1686],{},[603,2728,1318],{},[603,2730,785],{},[607,2732,1168],{},[2063,2734,2507],{},[603,2736,2510],{},[611,2738,2739],{"encoding":613},"\\oint_C \\vec F \\cdot d\\vec r = \\int_0^{2\\pi} \\begin{pmatrix} -\\sin t \\\\ \\cos t \\end{pmatrix} \\cdot \\begin{pmatrix} -\\sin t \\\\ \\cos t \\end{pmatrix} dt = \\int_0^{2\\pi} 1\\, dt = 2\\pi",[580,2741,2743,2836,2889,3059,3168,3256],{"className":2742,"ariaHidden":601},[618],[580,2744,2746,2749,2789,2792,2827,2830,2833],{"className":2745},[622],[580,2747],{"className":2748,"style":1381},[626],[580,2750,2752,2755],{"className":2751},[1385],[580,2753,2587],{"className":2754,"style":1391},[1385,1389,1390],[580,2756,2758],{"className":2757},[1395],[580,2759,2761,2781],{"className":2760},[636,1399],[580,2762,2764,2778],{"className":2763},[640],[580,2765,2767],{"className":2766,"style":1406},[644],[580,2768,2769,2772],{"style":1409},[580,2770],{"className":2771,"style":1413},[651],[580,2773,2775],{"className":2774},[1417,1418,1419,1420],[580,2776,1308],{"className":2777,"style":1424},[631,656,1420],[580,2779,1429],{"className":2780},[1428],[580,2782,2784],{"className":2783},[640],[580,2785,2787],{"className":2786,"style":1436},[644],[580,2788],{},[580,2790],{"className":2791,"style":1442},[1226],[580,2793,2795],{"className":2794},[631,632],[580,2796,2798],{"className":2797},[636],[580,2799,2801],{"className":2800},[640],[580,2802,2804,2812],{"className":2803,"style":627},[644],[580,2805,2806,2809],{"style":647},[580,2807],{"className":2808,"style":652},[651],[580,2810,605],{"className":2811,"style":657},[631,656],[580,2813,2814,2817],{"style":660},[580,2815],{"className":2816,"style":652},[651],[580,2818,2820],{"className":2819,"style":668},[667],[580,2821,2823],{"className":2822,"style":673},[672],[675,2824,2825],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,2826],{"d":686},[580,2828],{"className":2829,"style":1452},[1226],[580,2831,1315],{"className":2832},[1456],[580,2834],{"className":2835,"style":1452},[1226],[580,2837,2839,2842,2845,2880,2883,2886],{"className":2838},[622],[580,2840],{"className":2841,"style":814},[626],[580,2843,1318],{"className":2844},[631,656],[580,2846,2848],{"className":2847},[631,632],[580,2849,2851],{"className":2850},[636],[580,2852,2854],{"className":2853},[640],[580,2855,2857,2865],{"className":2856,"style":814},[644],[580,2858,2859,2862],{"style":647},[580,2860],{"className":2861,"style":652},[651],[580,2863,776],{"className":2864,"style":823},[631,656],[580,2866,2867,2870],{"style":647},[580,2868],{"className":2869,"style":652},[651],[580,2871,2873],{"className":2872,"style":832},[667],[580,2874,2876],{"className":2875,"style":673},[672],[675,2877,2878],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,2879],{"d":686},[580,2881],{"className":2882,"style":1227},[1226],[580,2884,1168],{"className":2885},[1231],[580,2887],{"className":2888,"style":1227},[1226],[580,2890,2892,2896,2955,2958,3050,3053,3056],{"className":2891},[622],[580,2893],{"className":2894,"style":2895},[626],"height:2.514em;vertical-align:-0.95em;",[580,2897,2899,2902],{"className":2898},[1385],[580,2900,1305],{"className":2901,"style":1391},[1385,1389,1390],[580,2903,2905],{"className":2904},[1395],[580,2906,2908,2947],{"className":2907},[636,1399],[580,2909,2911,2944],{"className":2910},[640],[580,2912,2915,2926],{"className":2913,"style":2914},[644],"height:1.564em;",[580,2916,2917,2920],{"style":1409},[580,2918],{"className":2919,"style":1413},[651],[580,2921,2923],{"className":2922},[1417,1418,1419,1420],[580,2924,2497],{"className":2925},[631,1420],[580,2927,2929,2932],{"style":2928},"top:-3.8129em;margin-right:0.05em;",[580,2930],{"className":2931,"style":1413},[651],[580,2933,2935],{"className":2934},[1417,1418,1419,1420],[580,2936,2938,2941],{"className":2937},[631,1420],[580,2939,2507],{"className":2940},[631,1420],[580,2942,2510],{"className":2943,"style":1814},[631,656,1420],[580,2945,1429],{"className":2946},[1428],[580,2948,2950],{"className":2949},[640],[580,2951,2953],{"className":2952,"style":1436},[644],[580,2954],{},[580,2956],{"className":2957,"style":1442},[1226],[580,2959,2962,2970,3044],{"className":2960},[2961],"minner",[580,2963,2967],{"className":2964,"style":2966},[843,2965],"delimcenter","top:0em;",[580,2968,782],{"className":2969},[1529,1419],[580,2971,2973],{"className":2972},[631],[580,2974,2976],{"className":2975},[2625],[580,2977,2980],{"className":2978},[2979],"col-align-c",[580,2981,2983,3035],{"className":2982},[636,1399],[580,2984,2986,3032],{"className":2985},[640],[580,2987,2990,3014],{"className":2988,"style":2989},[644],"height:1.45em;",[580,2991,2993,2996],{"style":2992},"top:-3.61em;",[580,2994],{"className":2995,"style":652},[651],[580,2997,2999,3002,3005,3008,3011],{"className":2998},[631],[580,3000,1349],{"className":3001},[631],[580,3003],{"className":3004,"style":1442},[1226],[580,3006,2341],{"className":3007},[1385],[580,3009],{"className":3010,"style":1442},[1226],[580,3012,785],{"className":3013},[631,656],[580,3015,3017,3020],{"style":3016},"top:-2.41em;",[580,3018],{"className":3019,"style":652},[651],[580,3021,3023,3026,3029],{"className":3022},[631],[580,3024,2329],{"className":3025},[1385],[580,3027],{"className":3028,"style":1442},[1226],[580,3030,785],{"className":3031},[631,656],[580,3033,1429],{"className":3034},[1428],[580,3036,3038],{"className":3037},[640],[580,3039,3042],{"className":3040,"style":3041},[644],"height:0.95em;",[580,3043],{},[580,3045,3047],{"className":3046,"style":2966},[850,2965],[580,3048,788],{"className":3049},[1529,1419],[580,3051],{"className":3052,"style":1452},[1226],[580,3054,1315],{"className":3055},[1456],[580,3057],{"className":3058,"style":1452},[1226],[580,3060,3062,3066,3150,3153,3156,3159,3162,3165],{"className":3061},[622],[580,3063],{"className":3064,"style":3065},[626],"height:2.4em;vertical-align:-0.95em;",[580,3067,3069,3075,3144],{"className":3068},[2961],[580,3070,3072],{"className":3071,"style":2966},[843,2965],[580,3073,782],{"className":3074},[1529,1419],[580,3076,3078],{"className":3077},[631],[580,3079,3081],{"className":3080},[2625],[580,3082,3084],{"className":3083},[2979],[580,3085,3087,3136],{"className":3086},[636,1399],[580,3088,3090,3133],{"className":3089},[640],[580,3091,3093,3116],{"className":3092,"style":2989},[644],[580,3094,3095,3098],{"style":2992},[580,3096],{"className":3097,"style":652},[651],[580,3099,3101,3104,3107,3110,3113],{"className":3100},[631],[580,3102,1349],{"className":3103},[631],[580,3105],{"className":3106,"style":1442},[1226],[580,3108,2341],{"className":3109},[1385],[580,3111],{"className":3112,"style":1442},[1226],[580,3114,785],{"className":3115},[631,656],[580,3117,3118,3121],{"style":3016},[580,3119],{"className":3120,"style":652},[651],[580,3122,3124,3127,3130],{"className":3123},[631],[580,3125,2329],{"className":3126},[1385],[580,3128],{"className":3129,"style":1442},[1226],[580,3131,785],{"className":3132},[631,656],[580,3134,1429],{"className":3135},[1428],[580,3137,3139],{"className":3138},[640],[580,3140,3142],{"className":3141,"style":3041},[644],[580,3143],{},[580,3145,3147],{"className":3146,"style":2966},[850,2965],[580,3148,788],{"className":3149},[1529,1419],[580,3151],{"className":3152,"style":1442},[1226],[580,3154,1318],{"className":3155},[631,656],[580,3157,785],{"className":3158},[631,656],[580,3160],{"className":3161,"style":1227},[1226],[580,3163,1168],{"className":3164},[1231],[580,3166],{"className":3167,"style":1227},[1226],[580,3169,3171,3175,3232,3235,3238,3241,3244,3247,3250,3253],{"className":3170},[622],[580,3172],{"className":3173,"style":3174},[626],"height:2.476em;vertical-align:-0.9119em;",[580,3176,3178,3181],{"className":3177},[1385],[580,3179,1305],{"className":3180,"style":1391},[1385,1389,1390],[580,3182,3184],{"className":3183},[1395],[580,3185,3187,3224],{"className":3186},[636,1399],[580,3188,3190,3221],{"className":3189},[640],[580,3191,3193,3204],{"className":3192,"style":2914},[644],[580,3194,3195,3198],{"style":1409},[580,3196],{"className":3197,"style":1413},[651],[580,3199,3201],{"className":3200},[1417,1418,1419,1420],[580,3202,2497],{"className":3203},[631,1420],[580,3205,3206,3209],{"style":2928},[580,3207],{"className":3208,"style":1413},[651],[580,3210,3212],{"className":3211},[1417,1418,1419,1420],[580,3213,3215,3218],{"className":3214},[631,1420],[580,3216,2507],{"className":3217},[631,1420],[580,3219,2510],{"className":3220,"style":1814},[631,656,1420],[580,3222,1429],{"className":3223},[1428],[580,3225,3227],{"className":3226},[640],[580,3228,3230],{"className":3229,"style":1436},[644],[580,3231],{},[580,3233],{"className":3234,"style":1442},[1226],[580,3236,2065],{"className":3237},[631],[580,3239],{"className":3240,"style":1442},[1226],[580,3242,1318],{"className":3243},[631,656],[580,3245,785],{"className":3246},[631,656],[580,3248],{"className":3249,"style":1227},[1226],[580,3251,1168],{"className":3252},[1231],[580,3254],{"className":3255,"style":1227},[1226],[580,3257,3259,3262,3265],{"className":3258},[622],[580,3260],{"className":3261,"style":2097},[626],[580,3263,2507],{"className":3264},[631],[580,3266,2510],{"className":3267,"style":1814},[631,656],[565,3269,3270],{},"Weil das Integral über eine geschlossene Kurve nicht null ist, ist dieses Feld kein Gradientenfeld.",[565,3272,3273,3274,3460,3461,3548,3549,3714,3715,3767,3768,3820,3821,4038],{},"Das Feld ",[580,3275,3277,3321],{"className":3276},[583],[580,3278,3280],{"className":3279},[587],[589,3281,3282],{"xmlns":591},[593,3283,3284,3318],{},[596,3285,3286,3292,3294,3296,3298,3300,3302,3304,3306,3312],{},[599,3287,3288,3290],{"accent":601},[603,3289,605],{},[607,3291,609],{},[607,3293,1168],{},[607,3295,782],{"stretchy":781},[2063,3297,2507],{},[603,3299,2131],{},[603,3301,2137],{},[607,3303,2134],{"separator":601},[1684,3305,2152],{},[2156,3307,3308,3310],{},[603,3309,2131],{},[2063,3311,2507],{},[2156,3313,3314,3316],{},[607,3315,788],{"stretchy":781},[603,3317,2162],{},[611,3319,3320],{"encoding":613},"\\vec F = (2xy,\\ x^2)^T",[580,3322,3324,3374],{"className":3323,"ariaHidden":601},[618],[580,3325,3327,3330,3365,3368,3371],{"className":3326},[622],[580,3328],{"className":3329,"style":627},[626],[580,3331,3333],{"className":3332},[631,632],[580,3334,3336],{"className":3335},[636],[580,3337,3339],{"className":3338},[640],[580,3340,3342,3350],{"className":3341,"style":627},[644],[580,3343,3344,3347],{"style":647},[580,3345],{"className":3346,"style":652},[651],[580,3348,605],{"className":3349,"style":657},[631,656],[580,3351,3352,3355],{"style":660},[580,3353],{"className":3354,"style":652},[651],[580,3356,3358],{"className":3357,"style":668},[667],[580,3359,3361],{"className":3360,"style":673},[672],[675,3362,3363],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,3364],{"d":686},[580,3366],{"className":3367,"style":1227},[1226],[580,3369,1168],{"className":3370},[1231],[580,3372],{"className":3373,"style":1227},[1226],[580,3375,3377,3380,3383,3386,3389,3392,3395,3398,3401,3431],{"className":3376},[622],[580,3378],{"className":3379,"style":2245},[626],[580,3381,782],{"className":3382},[843],[580,3384,2507],{"className":3385},[631],[580,3387,2131],{"className":3388},[631,656],[580,3390,2137],{"className":3391,"style":1814},[631,656],[580,3393,2134],{"className":3394},[2220],[580,3396,2152],{"className":3397},[1226],[580,3399],{"className":3400,"style":1442},[1226],[580,3402,3404,3407],{"className":3403},[631],[580,3405,2131],{"className":3406},[631,656],[580,3408,3410],{"className":3409},[1395],[580,3411,3413],{"className":3412},[636],[580,3414,3416],{"className":3415},[640],[580,3417,3420],{"className":3418,"style":3419},[644],"height:0.8141em;",[580,3421,3422,3425],{"style":2288},[580,3423],{"className":3424,"style":1413},[651],[580,3426,3428],{"className":3427},[1417,1418,1419,1420],[580,3429,2507],{"className":3430},[631,1420],[580,3432,3434,3437],{"className":3433},[850],[580,3435,788],{"className":3436},[850],[580,3438,3440],{"className":3439},[1395],[580,3441,3443],{"className":3442},[636],[580,3444,3446],{"className":3445},[640],[580,3447,3449],{"className":3448,"style":2285},[644],[580,3450,3451,3454],{"style":2288},[580,3452],{"className":3453,"style":1413},[651],[580,3455,3457],{"className":3456},[1417,1418,1419,1420],[580,3458,2162],{"className":3459,"style":657},[631,656,1420]," ist der Gradient von ",[580,3462,3464,3488],{"className":3463},[583],[580,3465,3467],{"className":3466},[587],[589,3468,3469],{"xmlns":591},[593,3470,3471,3485],{},[596,3472,3473,3475,3477,3483],{},[603,3474,1175],{},[607,3476,1168],{},[2156,3478,3479,3481],{},[603,3480,2131],{},[2063,3482,2507],{},[603,3484,2137],{},[611,3486,3487],{"encoding":613},"f = x^2 y",[580,3489,3491,3509],{"className":3490,"ariaHidden":601},[618],[580,3492,3494,3497,3500,3503,3506],{"className":3493},[622],[580,3495],{"className":3496,"style":1241},[626],[580,3498,1175],{"className":3499,"style":1248},[631,656],[580,3501],{"className":3502,"style":1227},[1226],[580,3504,1168],{"className":3505},[1231],[580,3507],{"className":3508,"style":1227},[1226],[580,3510,3512,3516,3545],{"className":3511},[622],[580,3513],{"className":3514,"style":3515},[626],"height:1.0085em;vertical-align:-0.1944em;",[580,3517,3519,3522],{"className":3518},[631],[580,3520,2131],{"className":3521},[631,656],[580,3523,3525],{"className":3524},[1395],[580,3526,3528],{"className":3527},[636],[580,3529,3531],{"className":3530},[640],[580,3532,3534],{"className":3533,"style":3419},[644],[580,3535,3536,3539],{"style":2288},[580,3537],{"className":3538,"style":1413},[651],[580,3540,3542],{"className":3541},[1417,1418,1419,1420],[580,3543,2507],{"className":3544},[631,1420],[580,3546,2137],{"className":3547,"style":1814},[631,656],". Längs der Strecke ",[580,3550,3552,3596],{"className":3551},[583],[580,3553,3555],{"className":3554},[587],[589,3556,3557],{"xmlns":591},[593,3558,3559,3593],{},[596,3560,3561,3567,3569,3571,3573,3575,3577,3579,3581,3583,3585,3587],{},[599,3562,3563,3565],{"accent":601},[603,3564,776],{},[607,3566,609],{},[607,3568,782],{"stretchy":781},[603,3570,785],{},[607,3572,788],{"stretchy":781},[607,3574,1168],{},[607,3576,782],{"stretchy":781},[603,3578,785],{},[607,3580,2134],{"separator":601},[1684,3582,2152],{},[2063,3584,2507],{},[603,3586,785],{},[2156,3588,3589,3591],{},[607,3590,788],{"stretchy":781},[603,3592,2162],{},[611,3594,3595],{"encoding":613},"\\vec r(t) = (t,\\ 2t)^T",[580,3597,3599,3658],{"className":3598,"ariaHidden":601},[618],[580,3600,3602,3605,3640,3643,3646,3649,3652,3655],{"className":3601},[622],[580,3603],{"className":3604,"style":801},[626],[580,3606,3608],{"className":3607},[631,632],[580,3609,3611],{"className":3610},[636],[580,3612,3614],{"className":3613},[640],[580,3615,3617,3625],{"className":3616,"style":814},[644],[580,3618,3619,3622],{"style":647},[580,3620],{"className":3621,"style":652},[651],[580,3623,776],{"className":3624,"style":823},[631,656],[580,3626,3627,3630],{"style":647},[580,3628],{"className":3629,"style":652},[651],[580,3631,3633],{"className":3632,"style":832},[667],[580,3634,3636],{"className":3635,"style":673},[672],[675,3637,3638],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,3639],{"d":686},[580,3641,782],{"className":3642},[843],[580,3644,785],{"className":3645},[631,656],[580,3647,788],{"className":3648},[850],[580,3650],{"className":3651,"style":1227},[1226],[580,3653,1168],{"className":3654},[1231],[580,3656],{"className":3657,"style":1227},[1226],[580,3659,3661,3664,3667,3670,3673,3676,3679,3682,3685],{"className":3660},[622],[580,3662],{"className":3663,"style":2245},[626],[580,3665,782],{"className":3666},[843],[580,3668,785],{"className":3669},[631,656],[580,3671,2134],{"className":3672},[2220],[580,3674,2152],{"className":3675},[1226],[580,3677],{"className":3678,"style":1442},[1226],[580,3680,2507],{"className":3681},[631],[580,3683,785],{"className":3684},[631,656],[580,3686,3688,3691],{"className":3687},[850],[580,3689,788],{"className":3690},[850],[580,3692,3694],{"className":3693},[1395],[580,3695,3697],{"className":3696},[636],[580,3698,3700],{"className":3699},[640],[580,3701,3703],{"className":3702,"style":2285},[644],[580,3704,3705,3708],{"style":2288},[580,3706],{"className":3707,"style":1413},[651],[580,3709,3711],{"className":3710},[1417,1418,1419,1420],[580,3712,2162],{"className":3713,"style":657},[631,656,1420]," von ",[580,3716,3718,3740],{"className":3717},[583],[580,3719,3721],{"className":3720},[587],[589,3722,3723],{"xmlns":591},[593,3724,3725,3737],{},[596,3726,3727,3729,3731,3733,3735],{},[607,3728,782],{"stretchy":781},[2063,3730,2497],{},[607,3732,2134],{"separator":601},[2063,3734,2497],{},[607,3736,788],{"stretchy":781},[611,3738,3739],{"encoding":613},"(0, 0)",[580,3741,3743],{"className":3742,"ariaHidden":601},[618],[580,3744,3746,3749,3752,3755,3758,3761,3764],{"className":3745},[622],[580,3747],{"className":3748,"style":801},[626],[580,3750,782],{"className":3751},[843],[580,3753,2497],{"className":3754},[631],[580,3756,2134],{"className":3757},[2220],[580,3759],{"className":3760,"style":1442},[1226],[580,3762,2497],{"className":3763},[631],[580,3765,788],{"className":3766},[850]," nach ",[580,3769,3771,3793],{"className":3770},[583],[580,3772,3774],{"className":3773},[587],[589,3775,3776],{"xmlns":591},[593,3777,3778,3790],{},[596,3779,3780,3782,3784,3786,3788],{},[607,3781,782],{"stretchy":781},[2063,3783,2065],{},[607,3785,2134],{"separator":601},[2063,3787,2507],{},[607,3789,788],{"stretchy":781},[611,3791,3792],{"encoding":613},"(1, 2)",[580,3794,3796],{"className":3795,"ariaHidden":601},[618],[580,3797,3799,3802,3805,3808,3811,3814,3817],{"className":3798},[622],[580,3800],{"className":3801,"style":801},[626],[580,3803,782],{"className":3804},[843],[580,3806,2065],{"className":3807},[631],[580,3809,2134],{"className":3810},[2220],[580,3812],{"className":3813,"style":1442},[1226],[580,3815,2507],{"className":3816},[631],[580,3818,788],{"className":3819},[850]," ist der Integrand ",[580,3822,3824,3874],{"className":3823},[583],[580,3825,3827],{"className":3826},[587],[589,3828,3829],{"xmlns":591},[593,3830,3831,3871],{},[596,3832,3833,3835,3837,3839,3841,3843,3845,3847,3850,3856,3858,3860,3862,3865],{},[2063,3834,2507],{},[603,3836,785],{},[607,3838,1315],{},[2063,3840,2507],{},[603,3842,785],{},[607,3844,1315],{},[2063,3846,2065],{},[607,3848,3849],{},"+",[2156,3851,3852,3854],{},[603,3853,785],{},[2063,3855,2507],{},[607,3857,1315],{},[2063,3859,2507],{},[607,3861,1168],{},[2063,3863,3864],{},"6",[2156,3866,3867,3869],{},[603,3868,785],{},[2063,3870,2507],{},[611,3872,3873],{"encoding":613},"2t \\cdot 2t \\cdot 1 + t^2 \\cdot 2 = 6t^2",[580,3875,3877,3898,3919,3938,3982,4000],{"className":3876,"ariaHidden":601},[618],[580,3878,3880,3883,3886,3889,3892,3895],{"className":3879},[622],[580,3881],{"className":3882,"style":2097},[626],[580,3884,2507],{"className":3885},[631],[580,3887,785],{"className":3888},[631,656],[580,3890],{"className":3891,"style":1452},[1226],[580,3893,1315],{"className":3894},[1456],[580,3896],{"className":3897,"style":1452},[1226],[580,3899,3901,3904,3907,3910,3913,3916],{"className":3900},[622],[580,3902],{"className":3903,"style":2097},[626],[580,3905,2507],{"className":3906},[631],[580,3908,785],{"className":3909},[631,656],[580,3911],{"className":3912,"style":1452},[1226],[580,3914,1315],{"className":3915},[1456],[580,3917],{"className":3918,"style":1452},[1226],[580,3920,3922,3926,3929,3932,3935],{"className":3921},[622],[580,3923],{"className":3924,"style":3925},[626],"height:0.7278em;vertical-align:-0.0833em;",[580,3927,2065],{"className":3928},[631],[580,3930],{"className":3931,"style":1452},[1226],[580,3933,3849],{"className":3934},[1456],[580,3936],{"className":3937,"style":1452},[1226],[580,3939,3941,3944,3973,3976,3979],{"className":3940},[622],[580,3942],{"className":3943,"style":3419},[626],[580,3945,3947,3950],{"className":3946},[631],[580,3948,785],{"className":3949},[631,656],[580,3951,3953],{"className":3952},[1395],[580,3954,3956],{"className":3955},[636],[580,3957,3959],{"className":3958},[640],[580,3960,3962],{"className":3961,"style":3419},[644],[580,3963,3964,3967],{"style":2288},[580,3965],{"className":3966,"style":1413},[651],[580,3968,3970],{"className":3969},[1417,1418,1419,1420],[580,3971,2507],{"className":3972},[631,1420],[580,3974],{"className":3975,"style":1452},[1226],[580,3977,1315],{"className":3978},[1456],[580,3980],{"className":3981,"style":1452},[1226],[580,3983,3985,3988,3991,3994,3997],{"className":3984},[622],[580,3986],{"className":3987,"style":2097},[626],[580,3989,2507],{"className":3990},[631],[580,3992],{"className":3993,"style":1227},[1226],[580,3995,1168],{"className":3996},[1231],[580,3998],{"className":3999,"style":1227},[1226],[580,4001,4003,4006,4009],{"className":4002},[622],[580,4004],{"className":4005,"style":3419},[626],[580,4007,3864],{"className":4008},[631],[580,4010,4012,4015],{"className":4011},[631],[580,4013,785],{"className":4014},[631,656],[580,4016,4018],{"className":4017},[1395],[580,4019,4021],{"className":4020},[636],[580,4022,4024],{"className":4023},[640],[580,4025,4027],{"className":4026,"style":3419},[644],[580,4028,4029,4032],{"style":2288},[580,4030],{"className":4031,"style":1413},[651],[580,4033,4035],{"className":4034},[1417,1418,1419,1420],[580,4036,2507],{"className":4037},[631,1420],", also",[580,4040,4042],{"className":4041},[1286],[580,4043,4045,4135],{"className":4044},[583],[580,4046,4048],{"className":4047},[587],[589,4049,4050],{"xmlns":591,"display":1295},[593,4051,4052,4132],{},[596,4053,4054,4060,4066,4068,4070,4076,4078,4086,4088,4094,4096,4098,4100,4102,4104,4106,4108,4110,4112,4114,4116,4118,4120,4122,4124,4126,4128,4130],{},[1301,4055,4056,4058],{},[607,4057,1305],{},[603,4059,1308],{},[599,4061,4062,4064],{"accent":601},[603,4063,605],{},[607,4065,609],{},[607,4067,1315],{},[603,4069,1318],{},[599,4071,4072,4074],{"accent":601},[603,4073,776],{},[607,4075,609],{},[607,4077,1168],{},[1695,4079,4080,4082,4084],{},[607,4081,1305],{},[2063,4083,2497],{},[2063,4085,2065],{},[2063,4087,3864],{},[2156,4089,4090,4092],{},[603,4091,785],{},[2063,4093,2507],{},[1684,4095,1686],{},[603,4097,1318],{},[603,4099,785],{},[607,4101,1168],{},[2063,4103,2507],{},[607,4105,1168],{},[603,4107,1175],{},[607,4109,782],{"stretchy":781},[2063,4111,2065],{},[607,4113,2134],{"separator":601},[2063,4115,2507],{},[607,4117,788],{"stretchy":781},[607,4119,1349],{},[603,4121,1175],{},[607,4123,782],{"stretchy":781},[2063,4125,2497],{},[607,4127,2134],{"separator":601},[2063,4129,2497],{},[607,4131,788],{"stretchy":781},[611,4133,4134],{"encoding":613},"\\int_C \\vec F \\cdot d\\vec r = \\int_0^1 6t^2\\, dt = 2 = f(1, 2) - f(0, 0)",[580,4136,4138,4231,4284,4396,4414,4450],{"className":4137,"ariaHidden":601},[618],[580,4139,4141,4144,4184,4187,4222,4225,4228],{"className":4140},[622],[580,4142],{"className":4143,"style":1381},[626],[580,4145,4147,4150],{"className":4146},[1385],[580,4148,1305],{"className":4149,"style":1391},[1385,1389,1390],[580,4151,4153],{"className":4152},[1395],[580,4154,4156,4176],{"className":4155},[636,1399],[580,4157,4159,4173],{"className":4158},[640],[580,4160,4162],{"className":4161,"style":1406},[644],[580,4163,4164,4167],{"style":1409},[580,4165],{"className":4166,"style":1413},[651],[580,4168,4170],{"className":4169},[1417,1418,1419,1420],[580,4171,1308],{"className":4172,"style":1424},[631,656,1420],[580,4174,1429],{"className":4175},[1428],[580,4177,4179],{"className":4178},[640],[580,4180,4182],{"className":4181,"style":1436},[644],[580,4183],{},[580,4185],{"className":4186,"style":1442},[1226],[580,4188,4190],{"className":4189},[631,632],[580,4191,4193],{"className":4192},[636],[580,4194,4196],{"className":4195},[640],[580,4197,4199,4207],{"className":4198,"style":627},[644],[580,4200,4201,4204],{"style":647},[580,4202],{"className":4203,"style":652},[651],[580,4205,605],{"className":4206,"style":657},[631,656],[580,4208,4209,4212],{"style":660},[580,4210],{"className":4211,"style":652},[651],[580,4213,4215],{"className":4214,"style":668},[667],[580,4216,4218],{"className":4217,"style":673},[672],[675,4219,4220],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,4221],{"d":686},[580,4223],{"className":4224,"style":1452},[1226],[580,4226,1315],{"className":4227},[1456],[580,4229],{"className":4230,"style":1452},[1226],[580,4232,4234,4237,4240,4275,4278,4281],{"className":4233},[622],[580,4235],{"className":4236,"style":814},[626],[580,4238,1318],{"className":4239},[631,656],[580,4241,4243],{"className":4242},[631,632],[580,4244,4246],{"className":4245},[636],[580,4247,4249],{"className":4248},[640],[580,4250,4252,4260],{"className":4251,"style":814},[644],[580,4253,4254,4257],{"style":647},[580,4255],{"className":4256,"style":652},[651],[580,4258,776],{"className":4259,"style":823},[631,656],[580,4261,4262,4265],{"style":647},[580,4263],{"className":4264,"style":652},[651],[580,4266,4268],{"className":4267,"style":832},[667],[580,4269,4271],{"className":4270,"style":673},[672],[675,4272,4273],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,4274],{"d":686},[580,4276],{"className":4277,"style":1227},[1226],[580,4279,1168],{"className":4280},[1231],[580,4282],{"className":4283,"style":1227},[1226],[580,4285,4287,4290,4341,4344,4347,4378,4381,4384,4387,4390,4393],{"className":4286},[622],[580,4288],{"className":4289,"style":3174},[626],[580,4291,4293,4296],{"className":4292},[1385],[580,4294,1305],{"className":4295,"style":1391},[1385,1389,1390],[580,4297,4299],{"className":4298},[1395],[580,4300,4302,4333],{"className":4301},[636,1399],[580,4303,4305,4330],{"className":4304},[640],[580,4306,4308,4319],{"className":4307,"style":2914},[644],[580,4309,4310,4313],{"style":1409},[580,4311],{"className":4312,"style":1413},[651],[580,4314,4316],{"className":4315},[1417,1418,1419,1420],[580,4317,2497],{"className":4318},[631,1420],[580,4320,4321,4324],{"style":2928},[580,4322],{"className":4323,"style":1413},[651],[580,4325,4327],{"className":4326},[1417,1418,1419,1420],[580,4328,2065],{"className":4329},[631,1420],[580,4331,1429],{"className":4332},[1428],[580,4334,4336],{"className":4335},[640],[580,4337,4339],{"className":4338,"style":1436},[644],[580,4340],{},[580,4342],{"className":4343,"style":1442},[1226],[580,4345,3864],{"className":4346},[631],[580,4348,4350,4353],{"className":4349},[631],[580,4351,785],{"className":4352},[631,656],[580,4354,4356],{"className":4355},[1395],[580,4357,4359],{"className":4358},[636],[580,4360,4362],{"className":4361},[640],[580,4363,4366],{"className":4364,"style":4365},[644],"height:0.8641em;",[580,4367,4369,4372],{"style":4368},"top:-3.113em;margin-right:0.05em;",[580,4370],{"className":4371,"style":1413},[651],[580,4373,4375],{"className":4374},[1417,1418,1419,1420],[580,4376,2507],{"className":4377},[631,1420],[580,4379],{"className":4380,"style":1442},[1226],[580,4382,1318],{"className":4383},[631,656],[580,4385,785],{"className":4386},[631,656],[580,4388],{"className":4389,"style":1227},[1226],[580,4391,1168],{"className":4392},[1231],[580,4394],{"className":4395,"style":1227},[1226],[580,4397,4399,4402,4405,4408,4411],{"className":4398},[622],[580,4400],{"className":4401,"style":2097},[626],[580,4403,2507],{"className":4404},[631],[580,4406],{"className":4407,"style":1227},[1226],[580,4409,1168],{"className":4410},[1231],[580,4412],{"className":4413,"style":1227},[1226],[580,4415,4417,4420,4423,4426,4429,4432,4435,4438,4441,4444,4447],{"className":4416},[622],[580,4418],{"className":4419,"style":801},[626],[580,4421,1175],{"className":4422,"style":1248},[631,656],[580,44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der Parabel ",[580,4481,4483,4531],{"className":4482},[583],[580,4484,4486],{"className":4485},[587],[589,4487,4488],{"xmlns":591},[593,4489,4490,4528],{},[596,4491,4492,4498,4500,4502,4504,4506,4508,4510,4512,4514,4516,4522],{},[599,4493,4494,4496],{"accent":601},[603,4495,776],{},[607,4497,609],{},[607,4499,782],{"stretchy":781},[603,4501,785],{},[607,4503,788],{"stretchy":781},[607,4505,1168],{},[607,4507,782],{"stretchy":781},[603,4509,785],{},[607,4511,2134],{"separator":601},[1684,4513,2152],{},[2063,4515,2507],{},[2156,4517,4518,4520],{},[603,4519,785],{},[2063,4521,2507],{},[2156,4523,4524,4526],{},[607,4525,788],{"stretchy":781},[603,4527,2162],{},[611,4529,4530],{"encoding":613},"\\vec r(t) = (t,\\ 2t^2)^T",[580,4532,4534,4593],{"className":4533,"ariaHidden":601},[618],[580,4535,4537,4540,4575,4578,4581,4584,4587,4590],{"className":4536},[622],[580,4538],{"className":4539,"style":801},[626],[580,4541,4543],{"className":4542},[631,632],[580,4544,4546],{"className":4545},[636],[580,4547,4549],{"className":4548},[640],[580,4550,4552,4560],{"className":4551,"style":814},[644],[580,4553,4554,4557],{"style":647},[580,4555],{"className":4556,"style":652},[651],[580,4558,776],{"className":4559,"style":823},[631,656],[580,4561,4562,4565],{"style":647},[580,4563],{"className":4564,"style":652},[651],[580,4566,4568],{"className":4567,"style":832},[667],[580,4569,4571],{"className":4570,"style":673},[672],[675,4572,4573],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,4574],{"d":686},[580,4576,782],{"className":4577},[843],[580,4579,785],{"className":4580},[631,656],[580,4582,788],{"className":4583},[850],[580,4585],{"className":4586,"style":1227},[1226],[580,4588,1168],{"className":4589},[1231],[580,4591],{"className":4592,"style":1227},[1226],[580,4594,4596,4599,4602,4605,4608,4611,4614,4617,4646],{"className":4595},[622],[580,4597],{"className":4598,"style":2245},[626],[580,4600,782],{"className":4601},[843],[580,4603,785],{"className":4604},[631,656],[580,4606,2134],{"className":4607},[2220],[580,4609,2152],{"className":4610},[1226],[580,4612],{"className":4613,"style":1442},[1226],[580,4615,2507],{"className":4616},[631],[580,4618,4620,4623],{"className":4619},[631],[580,4621,785],{"className":4622},[631,656],[580,4624,4626],{"className":4625},[1395],[580,4627,4629],{"className":4628},[636],[580,4630,4632],{"className":4631},[640],[580,4633,4635],{"className":4634,"style":3419},[644],[580,4636,4637,4640],{"style":2288},[580,4638],{"className":4639,"style":1413},[651],[580,4641,4643],{"className":4642},[1417,1418,1419,1420],[580,4644,2507],{"className":4645},[631,1420],[580,4647,4649,4652],{"className":4648},[850],[580,4650,788],{"className":4651},[850],[580,4653,4655],{"className":4654},[1395],[580,4656,4658],{"className":4657},[636],[580,4659,4661],{"className":4660},[640],[580,4662,4664],{"className":4663,"style":2285},[644],[580,4665,4666,4669],{"style":2288},[580,4667],{"className":4668,"style":1413},[651],[580,4670,4672],{"className":4671},[1417,1418,1419,1420],[580,4673,2162],{"className":4674,"style":657},[631,656,1420]," zwischen denselben Punkten ergibt sich mit dem Integranden ",[580,4677,4679,4701],{"className":4678},[583],[580,4680,4682],{"className":4681},[587],[589,4683,4684],{"xmlns":591},[593,4685,4686,4698],{},[596,4687,4688,4691],{},[2063,4689,4690],{},"8",[2156,4692,4693,4695],{},[603,4694,785],{},[2063,4696,4697],{},"3",[611,4699,4700],{"encoding":613},"8t^3",[580,4702,4704],{"className":4703,"ariaHidden":601},[618],[580,4705,4707,4710,4713],{"className":4706},[622],[580,4708],{"className":4709,"style":3419},[626],[580,4711,4690],{"className":4712},[631],[580,4714,4716,4719],{"className":4715},[631],[580,4717,785],{"className":4718},[631,656],[580,4720,4722],{"className":4721},[1395],[580,4723,4725],{"className":4724},[636],[580,4726,4728],{"className":4727},[640],[580,4729,4731],{"className":4730,"style":3419},[644],[580,4732,4733,4736],{"style":2288},[580,4734],{"className":4735,"style":1413},[651],[580,4737,4739],{"className":4738},[1417,1418,1419,1420],[580,4740,4697],{"className":4741},[631,1420]," ebenfalls ",[580,4744,4746,4759],{"className":4745},[583],[580,4747,4749],{"className":4748},[587],[589,4750,4751],{"xmlns":591},[593,4752,4753,4757],{},[596,4754,4755],{},[2063,4756,2507],{},[611,4758,2507],{"encoding":613},[580,4760,4762],{"className":4761,"ariaHidden":601},[618],[580,4763,4765,4768],{"className":4764},[622],[580,4766],{"className":4767,"style":2097},[626],[580,4769,2507],{"className":4770},[631],".",[560,4773,4775],{"id":4774},"typische-fehler","Typische Fehler",[4777,4778,4779,5024,5151,5154],"ul",{},[4780,4781,4782,4893,4894,5023],"li",{},[580,4783,4785,4812],{"className":4784},[583],[580,4786,4788],{"className":4787},[587],[589,4789,4790],{"xmlns":591},[593,4791,4792,4810],{},[596,4793,4794,4804,4806,4808],{},[599,4795,4796,4802],{"accent":601},[599,4797,4798,4800],{"accent":601},[603,4799,776],{},[607,4801,609],{},[607,4803,1019],{},[607,4805,782],{"stretchy":781},[603,4807,785],{},[607,4809,788],{"stretchy":781},[611,4811,1028],{"encoding":613},[580,4813,4815],{"className":4814,"ariaHidden":601},[618],[580,4816,4818,4821,4884,4887,4890],{"className":4817},[622],[580,4819],{"className":4820,"style":1038},[626],[580,4822,4824],{"className":4823},[631,632],[580,4825,4827],{"className":4826},[636],[580,4828,4830],{"className":4829},[640],[580,4831,4833,4873],{"className":4832,"style":1051},[644],[580,4834,4835,4838],{"style":647},[580,4836],{"className":4837,"style":652},[651],[580,4839,4841],{"className":4840},[631,632],[580,4842,4844],{"className":4843},[636],[580,4845,4847],{"className":4846},[640],[580,4848,4850,4858],{"className":4849,"style":814},[644],[580,4851,4852,4855],{"style":647},[580,4853],{"className":4854,"style":652},[651],[580,4856,776],{"className":4857,"style":823},[631,656],[580,4859,4860,4863],{"style":647},[580,4861],{"className":4862,"style":652},[651],[580,4864,4866],{"className":4865,"style":832},[667],[580,4867,4869],{"className":4868,"style":673},[672],[675,4870,4871],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,4872],{"d":686},[580,4874,4875,4878],{"style":1094},[580,4876],{"className":4877,"style":652},[651],[580,4879,4881],{"className":4880,"style":1101},[667],[580,4882,1019],{"className":4883},[631],[580,4885,782],{"className":4886},[843],[580,4888,785],{"className":4889},[631,656],[580,4891,788],{"className":4892},[850]," vergessen und nur ",[580,4895,4897,4931],{"className":4896},[583],[580,4898,4900],{"className":4899},[587],[589,4901,4902],{"xmlns":591},[593,4903,4904,4928],{},[596,4905,4906,4912,4914,4920,4922,4924,4926],{},[599,4907,4908,4910],{"accent":601},[603,4909,605],{},[607,4911,609],{},[607,4913,782],{"stretchy":781},[599,4915,4916,4918],{"accent":601},[603,4917,776],{},[607,4919,609],{},[607,4921,782],{"stretchy":781},[603,4923,785],{},[607,4925,788],{"stretchy":781},[607,4927,788],{"stretchy":781},[611,4929,4930],{"encoding":613},"\\vec F(\\vec r(t))",[580,4932,4934],{"className":4933,"ariaHidden":601},[618],[580,4935,4937,4940,4975,4978,5013,5016,5019],{"className":4936},[622],[580,4938],{"className":4939,"style":2175},[626],[580,4941,4943],{"className":4942},[631,632],[580,4944,4946],{"className":4945},[636],[580,4947,4949],{"className":4948},[640],[580,4950,4952,4960],{"className":4951,"style":627},[644],[580,4953,4954,4957],{"style":647},[580,4955],{"className":4956,"style":652},[651],[580,4958,605],{"className":4959,"style":657},[631,656],[580,4961,4962,4965],{"style":660},[580,4963],{"className":4964,"style":652},[651],[580,4966,4968],{"className":4967,"style":668},[667],[580,4969,4971],{"className":4970,"style":673},[672],[675,4972,4973],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,4974],{"d":686},[580,4976,782],{"className":4977},[843],[580,4979,4981],{"className":4980},[631,632],[580,4982,4984],{"className":4983},[636],[580,4985,4987],{"className":4986},[640],[580,4988,4990,4998],{"className":4989,"style":814},[644],[580,4991,4992,4995],{"style":647},[580,4993],{"className":4994,"style":652},[651],[580,4996,776],{"className":4997,"style":823},[631,656],[580,4999,5000,5003],{"style":647},[580,5001],{"className":5002,"style":652},[651],[580,5004,5006],{"className":5005,"style":832},[667],[580,5007,5009],{"className":5008,"style":673},[672],[675,5010,5011],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,5012],{"d":686},[580,5014,782],{"className":5015},[843],[580,5017,785],{"className":5018},[631,656],[580,5020,5022],{"className":5021},[850],"))"," integrieren. Das Ergebnis ist dann ein Vektor statt einer Zahl.",[4780,5025,5026,5027,5091,5092,5121,5122,5150],{},"Die Kurve nicht in ",[580,5028,5030,5047],{"className":5029},[583],[580,5031,5033],{"className":5032},[587],[589,5034,5035],{"xmlns":591},[593,5036,5037,5045],{},[596,5038,5039],{},[599,5040,5041,5043],{"accent":601},[603,5042,605],{},[607,5044,609],{},[611,5046,614],{"encoding":613},[580,5048,5050],{"className":5049,"ariaHidden":601},[618],[580,5051,5053,5056],{"className":5052},[622],[580,5054],{"className":5055,"style":627},[626],[580,5057,5059],{"className":5058},[631,632],[580,5060,5062],{"className":5061},[636],[580,5063,5065],{"className":5064},[640],[580,5066,5068,5076],{"className":5067,"style":627},[644],[580,5069,5070,5073],{"style":647},[580,5071],{"className":5072,"style":652},[651],[580,5074,605],{"className":5075,"style":657},[631,656],[580,5077,5078,5081],{"style":660},[580,5079],{"className":5080,"style":652},[651],[580,5082,5084],{"className":5083,"style":668},[667],[580,5085,5087],{"className":5086,"style":673},[672],[675,5088,5089],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,5090],{"d":686}," einsetzen, sondern ",[580,5093,5095,5108],{"className":5094},[583],[580,5096,5098],{"className":5097},[587],[589,5099,5100],{"xmlns":591},[593,5101,5102,5106],{},[596,5103,5104],{},[603,5105,2131],{},[611,5107,2131],{"encoding":613},[580,5109,5111],{"className":5110,"ariaHidden":601},[618],[580,5112,5114,5118],{"className":5113},[622],[580,5115],{"className":5116,"style":5117},[626],"height:0.4306em;",[580,5119,2131],{"className":5120},[631,656]," und ",[580,5123,5125,5138],{"className":5124},[583],[580,5126,5128],{"className":5127},[587],[589,5129,5130],{"xmlns":591},[593,5131,5132,5136],{},[596,5133,5134],{},[603,5135,2137],{},[611,5137,2137],{"encoding":613},[580,5139,5141],{"className":5140,"ariaHidden":601},[618],[580,5142,5144,5147],{"className":5143},[622],[580,5145],{"className":5146,"style":2078},[626],[580,5148,2137],{"className":5149,"style":1814},[631,656]," stehen lassen.",[4780,5152,5153],{},"Die Durchlaufrichtung ignorieren. Bei umgekehrter Richtung ändert sich das Vorzeichen.",[4780,5155,5156,5157,5221],{},"Wegunabhängigkeit annehmen, ohne zu prüfen, ob ",[580,5158,5160,5177],{"className":5159},[583],[580,5161,5163],{"className":5162},[587],[589,5164,5165],{"xmlns":591},[593,5166,5167,5175],{},[596,5168,5169],{},[599,5170,5171,5173],{"accent":601},[603,5172,605],{},[607,5174,609],{},[611,5176,614],{"encoding":613},[580,5178,5180],{"className":5179,"ariaHidden":601},[618],[580,5181,5183,5186],{"className":5182},[622],[580,5184],{"className":5185,"style":627},[626],[580,5187,5189],{"className":5188},[631,632],[580,5190,5192],{"className":5191},[636],[580,5193,5195],{"className":5194},[640],[580,5196,5198,5206],{"className":5197,"style":627},[644],[580,5199,5200,5203],{"style":647},[580,5201],{"className":5202,"style":652},[651],[580,5204,605],{"className":5205,"style":657},[631,656],[580,5207,5208,5211],{"style":660},[580,5209],{"className":5210,"style":652},[651],[580,5212,5214],{"className":5213,"style":668},[667],[580,5215,5217],{"className":5216,"style":673},[672],[675,5218,5219],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,5220],{"d":686}," ein Gradientenfeld ist.",{"title":5223,"searchDepth":5224,"depth":5224,"links":5225},"",2,[5226,5227,5228],{"id":562,"depth":5224,"text":563},{"id":2104,"depth":5224,"text":2105},{"id":4774,"depth":5224,"text":4775},[5230,5232,5235,5238,5240,5242,5245],{"lhs":5231,"rhs":2065},"(-sin(t))*(-sin(t)) + cos(t)*cos(t)",{"lhs":5233,"rhs":5234},"round(sum(map(0:999, f(k) = sin((k + 0.5)*2*pi\u002F1000)^2 + cos((k + 0.5)*2*pi\u002F1000)^2)) * 2*pi\u002F1000, 6)","round(2*pi, 6)",{"lhs":5236,"rhs":5237},"2*t*(2*t)*1 + t^2*2","6*t^2",{"lhs":5239,"rhs":2507},"round(sum(map(0:999, f(k) = 6*((k + 0.5)\u002F1000)^2)) \u002F 1000, 4)",{"lhs":5241,"rhs":2507},"1^2*2 - 0^2*0",{"lhs":5243,"rhs":5244},"2*t*(2*t^2)*1 + t^2*4*t","8*t^3",{"lhs":5246,"rhs":2507},"round(sum(map(0:999, f(k) = 8*((k + 0.5)\u002F1000)^3)) \u002F 1000, 4)","\\vec{r}\\colon [a, b] \\to \\mathbb{R}^n \\text{ stückweise stetig differenzierbare Parametrisierung von } C,\\ \\vec{F} \\text{ stetig auf } C","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>r\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\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>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003Cmo>→\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{r}\\colon [a, b] \\to 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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=\"mopen\">[\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">]\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 class=\"katex\">stückweise stetig differenzierbare Parametrisierung von\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>C\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">C,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\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>\u003Cmover accent=\"true\">\u003Cmi>F\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{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:0.9663em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9663em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2523em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1522em;\">\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 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style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1799em;\">\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 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