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das auf einer Umgebung von ",[580,1033,1035,1048],{"className":1034},[583],[580,1036,1038],{"className":1037},[587],[589,1039,1040],{"xmlns":591},[593,1041,1042,1046],{},[596,1043,1044],{},[603,1045,770],{},[611,1047,770],{"encoding":613},[580,1049,1051],{"className":1050,"ariaHidden":601},[618],[580,1052,1054,1058],{"className":1053},[622],[580,1055],{"className":1056,"style":1057},[626],"height:0.6833em;",[580,1059,770],{"className":1060,"style":801},[631,656]," stetig differenzierbar ist (",[580,1063,1065,1094],{"className":1064},[583],[580,1066,1068],{"className":1067},[587],[589,1069,1070],{"xmlns":591},[593,1071,1072,1091],{},[596,1073,1074,1080,1083],{},[599,1075,1076,1078],{"accent":601},[603,1077,605],{},[607,1079,609],{},[607,1081,1082],{},"∈",[775,1084,1085,1088],{},[603,1086,1087],{},"C",[782,1089,1090],{},"1",[611,1092,1093],{"encoding":613},"\\vec F \\in C^1",[580,1095,1097,1148],{"className":1096,"ariaHidden":601},[618],[580,1098,1100,1104,1139,1142,1145],{"className":1099},[622],[580,1101],{"className":1102,"style":1103},[626],"height:1.0054em;vertical-align:-0.0391em;",[580,1105,1107],{"className":1106},[631,632],[580,1108,1110],{"className":1109},[636],[580,1111,1113],{"className":1112},[640],[580,1114,1116,1124],{"className":1115,"style":627},[644],[580,1117,1118,1121],{"style":647},[580,1119],{"className":1120,"style":652},[651],[580,1122,605],{"className":1123,"style":657},[631,656],[580,1125,1126,1129],{"style":660},[580,1127],{"className":1128,"style":652},[651],[580,1130,1132],{"className":1131,"style":668},[667],[580,1133,1135],{"className":1134,"style":673},[672],[675,1136,1137],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,1138],{"d":686},[580,1140],{"className":1141,"style":806},[805],[580,1143,1082],{"className":1144},[810],[580,1146],{"className":1147,"style":806},[805],[580,1149,1151,1154],{"className":1150},[622],[580,1152],{"className":1153,"style":820},[626],[580,1155,1157,1161],{"className":1156},[631],[580,1158,1087],{"className":1159,"style":1160},[631,656],"margin-right:0.0715em;",[580,1162,1164],{"className":1163},[831],[580,1165,1167],{"className":1166},[636],[580,1168,1170],{"className":1169},[640],[580,1171,1173],{"className":1172,"style":820},[644],[580,1174,1175,1178],{"style":843},[580,1176],{"className":1177,"style":847},[651],[580,1179,1181],{"className":1180},[851,852,853,854],[580,1182,1090],{"className":1183},[631,854],").",[565,1186,1187],{},"Der Satz wird in beide Richtungen genutzt:",[1189,1190,1191,1195],"ul",{},[1192,1193,1194],"li",{},"Ein schwieriges Oberflächenintegral (z.B. über die sechs Seiten eines Quaders) wird zu einem einfachen Volumenintegral.",[1192,1196,1197],{},"Aus lokalen Erhaltungsgesetzen (Masse, Ladung, Energie) wird eine globale Bilanz und umgekehrt.",[565,1199,1200,1201,1265,1266,1269,1270,1636],{},"Ist ",[580,1202,1204,1221],{"className":1203},[583],[580,1205,1207],{"className":1206},[587],[589,1208,1209],{"xmlns":591},[593,1210,1211,1219],{},[596,1212,1213],{},[599,1214,1215,1217],{"accent":601},[603,1216,605],{},[607,1218,609],{},[611,1220,614],{"encoding":613},[580,1222,1224],{"className":1223,"ariaHidden":601},[618],[580,1225,1227,1230],{"className":1226},[622],[580,1228],{"className":1229,"style":627},[626],[580,1231,1233],{"className":1232},[631,632],[580,1234,1236],{"className":1235},[636],[580,1237,1239],{"className":1238},[640],[580,1240,1242,1250],{"className":1241,"style":627},[644],[580,1243,1244,1247],{"style":647},[580,1245],{"className":1246,"style":652},[651],[580,1248,605],{"className":1249,"style":657},[631,656],[580,1251,1252,1255],{"style":660},[580,1253],{"className":1254,"style":652},[651],[580,1256,1258],{"className":1257,"style":668},[667],[580,1259,1261],{"className":1260,"style":673},[672],[675,1262,1263],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,1264],{"d":686}," quellenfrei, ist der Fluss durch jede geschlossene Fläche null. Die Normale muss ",[569,1267,1268],{},"nach außen"," zeigen, und die Fläche muss den Bereich vollständig umschließen. Die ebene Version ist der Satz von Green in Flussform: ",[580,1271,1273,1352],{"className":1272},[583],[580,1274,1276],{"className":1275},[587],[589,1277,1278],{"xmlns":591},[593,1279,1280,1349],{},[596,1281,1282,1291,1294,1297,1303,1307,1310,1313,1316,1327,1333,1336,1342,1344,1346],{},[1283,1284,1285,1288],"msub",{},[607,1286,1287],{},"∬",[603,1289,1290],{},"D",[603,1292,1293],{"mathvariant":873},"div",[607,1295,1296],{},"⁡",[599,1298,1299,1301],{"accent":601},[603,1300,605],{},[607,1302,609],{},[1304,1305,1306],"mtext",{}," ",[603,1308,1309],{},"d",[603,1311,1312],{},"A",[607,1314,1315],{},"=",[1283,1317,1318,1321],{},[607,1319,1320],{},"∮",[596,1322,1323,1325],{},[603,1324,874],{"mathvariant":873},[603,1326,1290],{},[599,1328,1329,1331],{"accent":601},[603,1330,605],{},[607,1332,609],{},[607,1334,1335],{},"⋅",[599,1337,1338,1340],{"accent":601},[603,1339,914],{},[607,1341,609],{},[1304,1343,1306],{},[603,1345,1309],{},[603,1347,1348],{},"s",[611,1350,1351],{"encoding":613},"\\iint_D \\operatorname{div} \\vec F\\, dA = \\oint_{\\partial D} \\vec F \\cdot \\vec n\\, ds",[580,1353,1355,1481,1586],{"className":1354,"ariaHidden":601},[618],[580,1356,1358,1362,1413,1417,1425,1428,1463,1466,1469,1472,1475,1478],{"className":1357},[622],[580,1359],{"className":1360,"style":1361},[626],"height:1.322em;vertical-align:-0.3557em;",[580,1363,1366,1372],{"className":1364},[1365],"mop",[580,1367,1287],{"className":1368,"style":1371},[1365,1369,1370],"op-symbol","small-op","margin-right:0.1945em;position:relative;top:-0.0005em;",[580,1373,1375],{"className":1374},[831],[580,1376,1379,1404],{"className":1377},[636,1378],"vlist-t2",[580,1380,1382,1399],{"className":1381},[640],[580,1383,1386],{"className":1384,"style":1385},[644],"height:0.1226em;",[580,1387,1389,1392],{"style":1388},"top:-2.3443em;margin-left:-0.1945em;margin-right:0.05em;",[580,1390],{"className":1391,"style":847},[651],[580,1393,1395],{"className":1394},[851,852,853,854],[580,1396,1290],{"className":1397,"style":1398},[631,656,854],"margin-right:0.0278em;",[580,1400,1403],{"className":1401},[1402],"vlist-s","​",[580,1405,1407],{"className":1406},[640],[580,1408,1411],{"className":1409,"style":1410},[644],"height:0.3557em;",[580,1412],{},[580,1414],{"className":1415,"style":1416},[805],"margin-right:0.1667em;",[580,1418,1420],{"className":1419},[1365],[580,1421,1293],{"className":1422,"style":1424},[631,1423],"mathrm","margin-right:0.0139em;",[580,1426],{"className":1427,"style":1416},[805],[580,1429,1431],{"className":1430},[631,632],[580,1432,1434],{"className":1433},[636],[580,1435,1437],{"className":1436},[640],[580,1438,1440,1448],{"className":1439,"style":627},[644],[580,1441,1442,1445],{"style":647},[580,1443],{"className":1444,"style":652},[651],[580,1446,605],{"className":1447,"style":657},[631,656],[580,1449,1450,1453],{"style":660},[580,1451],{"className":1452,"style":652},[651],[580,1454,1456],{"className":1455,"style":668},[667],[580,1457,1459],{"className":1458,"style":673},[672],[675,1460,1461],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,1462],{"d":686},[580,1464],{"className":1465,"style":1416},[805],[580,1467,1309],{"className":1468},[631,656],[580,1470,1312],{"className":1471},[631,656],[580,1473],{"className":1474,"style":806},[805],[580,1476,1315],{"className":1477},[810],[580,1479],{"className":1480,"style":806},[805],[580,1482,1484,1488,1538,1541,1576,1579,1583],{"className":1483},[622],[580,1485],{"className":1486,"style":1487},[626],"height:1.3221em;vertical-align:-0.3558em;",[580,1489,1491,1495],{"className":1490},[1365],[580,1492,1320],{"className":1493,"style":1494},[1365,1369,1370],"margin-right:0.1945em;position:relative;top:-0.0006em;",[580,1496,1498],{"className":1497},[831],[580,1499,1501,1529],{"className":1500},[636,1378],[580,1502,1504,1526],{"className":1503},[640],[580,1505,1508],{"className":1506,"style":1507},[644],"height:0.1303em;",[580,1509,1511,1514],{"style":1510},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[580,1512],{"className":1513,"style":847},[651],[580,1515,1517],{"className":1516},[851,852,853,854],[580,1518,1520,1523],{"className":1519},[631,854],[580,1521,874],{"className":1522,"style":893},[631,854],[580,1524,1290],{"className":1525,"style":1398},[631,656,854],[580,1527,1403],{"className":1528},[1402],[580,1530,1532],{"className":1531},[640],[580,1533,1536],{"className":1534,"style":1535},[644],"height:0.3558em;",[580,1537],{},[580,1539],{"className":1540,"style":1416},[805],[580,1542,1544],{"className":1543},[631,632],[580,1545,1547],{"className":1546},[636],[580,1548,1550],{"className":1549},[640],[580,1551,1553,1561],{"className":1552,"style":627},[644],[580,1554,1555,1558],{"style":647},[580,1556],{"className":1557,"style":652},[651],[580,1559,605],{"className":1560,"style":657},[631,656],[580,1562,1563,1566],{"style":660},[580,1564],{"className":1565,"style":652},[651],[580,1567,1569],{"className":1568,"style":668},[667],[580,1570,1572],{"className":1571,"style":673},[672],[675,1573,1574],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,1575],{"d":686},[580,1577],{"className":1578,"style":801},[805],[580,1580,1335],{"className":1581},[1582],"mbin",[580,1584],{"className":1585,"style":801},[805],[580,1587,1589,1592,1627,1630,1633],{"className":1588},[622],[580,1590],{"className":1591,"style":929},[626],[580,1593,1595],{"className":1594},[631,632],[580,1596,1598],{"className":1597},[636],[580,1599,1601],{"className":1600},[640],[580,1602,1604,1612],{"className":1603,"style":929},[644],[580,1605,1606,1609],{"style":647},[580,1607],{"className":1608,"style":652},[651],[580,1610,914],{"className":1611},[631,656],[580,1613,1614,1617],{"style":647},[580,1615],{"className":1616,"style":652},[651],[580,1618,1620],{"className":1619,"style":958},[667],[580,1621,1623],{"className":1622,"style":673},[672],[675,1624,1625],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,1626],{"d":686},[580,1628],{"className":1629,"style":1416},[805],[580,1631,1309],{"className":1632},[631,656],[580,1634,1348],{"className":1635},[631,656],".",[560,1638,1640],{"id":1639},"beispiele","Beispiele",[565,1642,1643,1644,1812,1813,1842,1843,1944],{},"Für ",[580,1645,1647,1693],{"className":1646},[583],[580,1648,1650],{"className":1649},[587],[589,1651,1652],{"xmlns":591},[593,1653,1654,1690],{},[596,1655,1656,1662,1664,1668,1671,1674,1677,1679,1682],{},[599,1657,1658,1660],{"accent":601},[603,1659,605],{},[607,1661,609],{},[607,1663,1315],{},[607,1665,1667],{"stretchy":1666},"false","(",[603,1669,1670],{},"x",[607,1672,1673],{"separator":601},",",[603,1675,1676],{},"y",[607,1678,1673],{"separator":601},[603,1680,1681],{},"z",[775,1683,1684,1687],{},[607,1685,1686],{"stretchy":1666},")",[603,1688,1689],{},"T",[611,1691,1692],{"encoding":613},"\\vec F = (x, y, z)^T",[580,1694,1696,1746],{"className":1695,"ariaHidden":601},[618],[580,1697,1699,1702,1737,1740,1743],{"className":1698},[622],[580,1700],{"className":1701,"style":627},[626],[580,1703,1705],{"className":1704},[631,632],[580,1706,1708],{"className":1707},[636],[580,1709,1711],{"className":1710},[640],[580,1712,1714,1722],{"className":1713,"style":627},[644],[580,1715,1716,1719],{"style":647},[580,1717],{"className":1718,"style":652},[651],[580,1720,605],{"className":1721,"style":657},[631,656],[580,1723,1724,1727],{"style":660},[580,1725],{"className":1726,"style":652},[651],[580,1728,1730],{"className":1729,"style":668},[667],[580,1731,1733],{"className":1732,"style":673},[672],[675,1734,1735],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,1736],{"d":686},[580,1738],{"className":1739,"style":806},[805],[580,1741,1315],{"className":1742},[810],[580,1744],{"className":1745,"style":806},[805],[580,1747,1749,1753,1757,1760,1764,1767,1771,1774,1777,1781],{"className":1748},[622],[580,1750],{"className":1751,"style":1752},[626],"height:1.0913em;vertical-align:-0.25em;",[580,1754,1667],{"className":1755},[1756],"mopen",[580,1758,1670],{"className":1759},[631,656],[580,1761,1673],{"className":1762},[1763],"mpunct",[580,1765],{"className":1766,"style":1416},[805],[580,1768,1676],{"className":1769,"style":1770},[631,656],"margin-right:0.0359em;",[580,1772,1673],{"className":1773},[1763],[580,1775],{"className":1776,"style":1416},[805],[580,1778,1681],{"className":1779,"style":1780},[631,656],"margin-right:0.044em;",[580,1782,1785,1788],{"className":1783},[1784],"mclose",[580,1786,1686],{"className":1787},[1784],[580,1789,1791],{"className":1790},[831],[580,1792,1794],{"className":1793},[636],[580,1795,1797],{"className":1796},[640],[580,1798,1801],{"className":1799,"style":1800},[644],"height:0.8413em;",[580,1802,1803,1806],{"style":843},[580,1804],{"className":1805,"style":847},[651],[580,1807,1809],{"className":1808},[851,852,853,854],[580,1810,1689],{"className":1811,"style":657},[631,656,854]," und die Kugel mit Radius ",[580,1814,1816,1829],{"className":1815},[583],[580,1817,1819],{"className":1818},[587],[589,1820,1821],{"xmlns":591},[593,1822,1823,1827],{},[596,1824,1825],{},[603,1826,780],{},[611,1828,780],{"encoding":613},[580,1830,1832],{"className":1831,"ariaHidden":601},[618],[580,1833,1835,1838],{"className":1834},[622],[580,1836],{"className":1837,"style":1057},[626],[580,1839,780],{"className":1840,"style":1841},[631,656],"margin-right:0.0077em;"," ist ",[580,1844,1846,1872],{"className":1845},[583],[580,1847,1849],{"className":1848},[587],[589,1850,1851],{"xmlns":591},[593,1852,1853,1869],{},[596,1854,1855,1857,1859,1865,1867],{},[603,1856,1293],{"mathvariant":873},[607,1858,1296],{},[599,1860,1861,1863],{"accent":601},[603,1862,605],{},[607,1864,609],{},[607,1866,1315],{},[782,1868,784],{},[611,1870,1871],{"encoding":613},"\\operatorname{div} \\vec F = 3",[580,1873,1875,1934],{"className":1874,"ariaHidden":601},[618],[580,1876,1878,1881,1887,1890,1925,1928,1931],{"className":1877},[622],[580,1879],{"className":1880,"style":627},[626],[580,1882,1884],{"className":1883},[1365],[580,1885,1293],{"className":1886,"style":1424},[631,1423],[580,1888],{"className":1889,"style":1416},[805],[580,1891,1893],{"className":1892},[631,632],[580,1894,1896],{"className":1895},[636],[580,1897,1899],{"className":1898},[640],[580,1900,1902,1910],{"className":1901,"style":627},[644],[580,1903,1904,1907],{"style":647},[580,1905],{"className":1906,"style":652},[651],[580,1908,605],{"className":1909,"style":657},[631,656],[580,1911,1912,1915],{"style":660},[580,1913],{"className":1914,"style":652},[651],[580,1916,1918],{"className":1917,"style":668},[667],[580,1919,1921],{"className":1920,"style":673},[672],[675,1922,1923],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,1924],{"d":686},[580,1926],{"className":1927,"style":806},[805],[580,1929,1315],{"className":1930},[810],[580,1932],{"className":1933,"style":806},[805],[580,1935,1937,1941],{"className":1936},[622],[580,1938],{"className":1939,"style":1940},[626],"height:0.6444em;",[580,1942,784],{"className":1943},[631],", also",[580,1946,1949],{"className":1947},[1948],"katex-display",[580,1950,1952,2015],{"className":1951},[583],[580,1953,1955],{"className":1954},[587],[589,1956,1958],{"xmlns":591,"display":1957},"block",[593,1959,1960,2012],{},[596,1961,1962,1969,1971,1973,1975,1977,1979,1981,1983,1991,1994,2000,2002,2004,2006],{},[1283,1963,1964,1967],{},[607,1965,1966],{},"∭",[603,1968,770],{},[782,1970,784],{},[1304,1972,1306],{},[603,1974,1309],{},[603,1976,770],{},[607,1978,1315],{},[782,1980,784],{},[607,1982,1335],{},[1984,1985,1986,1989],"mfrac",{},[782,1987,1988],{},"4",[782,1990,784],{},[603,1992,1993],{},"π",[775,1995,1996,1998],{},[603,1997,780],{},[782,1999,784],{},[607,2001,1315],{},[782,2003,1988],{},[603,2005,1993],{},[775,2007,2008,2010],{},[603,2009,780],{},[782,2011,784],{},[611,2013,2014],{"encoding":613},"\\iiint_V 3\\, dV = 3 \\cdot \\frac{4}{3}\\pi R^3 = 4\\pi R^3",[580,2016,2018,2094,2112,2232],{"className":2017,"ariaHidden":601},[618],[580,2019,2021,2025,2070,2073,2076,2079,2082,2085,2088,2091],{"className":2020},[622],[580,2022],{"className":2023,"style":2024},[626],"height:2.2717em;vertical-align:-0.9117em;",[580,2026,2028,2033],{"className":2027},[1365],[580,2029,1966],{"className":2030,"style":2032},[1365,1369,2031],"large-op","margin-right:0.4445em;position:relative;top:-0.001em;",[580,2034,2036],{"className":2035},[831],[580,2037,2039,2061],{"className":2038},[636,1378],[580,2040,2042,2058],{"className":2041},[640],[580,2043,2046],{"className":2044,"style":2045},[644],"height:-0.4334em;",[580,2047,2049,2052],{"style":2048},"top:-1.7883em;margin-left:-0.4445em;margin-right:0.05em;",[580,2050],{"className":2051,"style":847},[651],[580,2053,2055],{"className":2054},[851,852,853,854],[580,2056,770],{"className":2057,"style":801},[631,656,854],[580,2059,1403],{"className":2060},[1402],[580,2062,2064],{"className":2063},[640],[580,2065,2068],{"className":2066,"style":2067},[644],"height:0.9117em;",[580,2069],{},[580,2071],{"className":2072,"style":1416},[805],[580,2074,784],{"className":2075},[631],[580,2077],{"className":2078,"style":1416},[805],[580,2080,1309],{"className":2081},[631,656],[580,2083,770],{"className":2084,"style":801},[631,656],[580,2086],{"className":2087,"style":806},[805],[580,2089,1315],{"className":2090},[810],[580,2092],{"className":2093,"style":806},[805],[580,2095,2097,2100,2103,2106,2109],{"className":2096},[622],[580,2098],{"className":2099,"style":1940},[626],[580,2101,784],{"className":2102},[631],[580,2104],{"className":2105,"style":801},[805],[580,2107,1335],{"className":2108},[1582],[580,2110],{"className":2111,"style":801},[805],[580,2113,2115,2119,2189,2192,2223,2226,2229],{"className":2114},[622],[580,2116],{"className":2117,"style":2118},[626],"height:2.0074em;vertical-align:-0.686em;",[580,2120,2122,2126,2186],{"className":2121},[631],[580,2123],{"className":2124},[1756,2125],"nulldelimiter",[580,2127,2129],{"className":2128},[1984],[580,2130,2132,2177],{"className":2131},[636,1378],[580,2133,2135,2174],{"className":2134},[640],[580,2136,2139,2151,2162],{"className":2137,"style":2138},[644],"height:1.3214em;",[580,2140,2142,2145],{"style":2141},"top:-2.314em;",[580,2143],{"className":2144,"style":652},[651],[580,2146,2148],{"className":2147},[631],[580,2149,784],{"className":2150},[631],[580,2152,2154,2157],{"style":2153},"top:-3.23em;",[580,2155],{"className":2156,"style":652},[651],[580,2158],{"className":2159,"style":2161},[2160],"frac-line","border-bottom-width:0.04em;",[580,2163,2165,2168],{"style":2164},"top:-3.677em;",[580,2166],{"className":2167,"style":652},[651],[580,2169,2171],{"className":2170},[631],[580,2172,1988],{"className":2173},[631],[580,2175,1403],{"className":2176},[1402],[580,2178,2180],{"className":2179},[640],[580,2181,2184],{"className":2182,"style":2183},[644],"height:0.686em;",[580,2185],{},[580,2187],{"className":2188},[1784,2125],[580,2190,1993],{"className":2191,"style":1770},[631,656],[580,2193,2195,2198],{"className":2194},[631],[580,2196,780],{"className":2197,"style":1841},[631,656],[580,2199,2201],{"className":2200},[831],[580,2202,2204],{"className":2203},[636],[580,2205,2207],{"className":2206},[640],[580,2208,2211],{"className":2209,"style":2210},[644],"height:0.8641em;",[580,2212,2214,2217],{"style":2213},"top:-3.113em;margin-right:0.05em;",[580,2215],{"className":2216,"style":847},[651],[580,2218,2220],{"className":2219},[851,852,853,854],[580,2221,784],{"className":2222},[631,854],[580,2224],{"className":2225,"style":806},[805],[580,2227,1315],{"className":2228},[810],[580,2230],{"className":2231,"style":806},[805],[580,2233,2235,2238,2241,2244],{"className":2234},[622],[580,2236],{"className":2237,"style":2210},[626],[580,2239,1988],{"className":2240},[631],[580,2242,1993],{"className":2243,"style":1770},[631,656],[580,2245,2247,2250],{"className":2246},[631],[580,2248,780],{"className":2249,"style":1841},[631,656],[580,2251,2253],{"className":2252},[831],[580,2254,2256],{"className":2255},[636],[580,2257,2259],{"className":2258},[640],[580,2260,2262],{"className":2261,"style":2210},[644],[580,2263,2264,2267],{"style":2213},[580,2265],{"className":2266,"style":847},[651],[580,2268,2270],{"className":2269},[851,852,853,854],[580,2271,784],{"className":2272},[631,854],[565,2274,2275,2276,2508,2509,2867,2868,3021,3022,3073,3074,1636],{},"Zur Kontrolle direkt: Auf der Kugeloberfläche ist ",[580,2277,2279,2323],{"className":2278},[583],[580,2280,2282],{"className":2281},[587],[589,2283,2284],{"xmlns":591},[593,2285,2286,2320],{},[596,2287,2288,2294,2296,2302,2304,2306,2308,2310,2312,2314],{},[599,2289,2290,2292],{"accent":601},[603,2291,914],{},[607,2293,609],{},[607,2295,1315],{},[1984,2297,2298,2300],{},[782,2299,1090],{},[603,2301,780],{},[607,2303,1667],{"stretchy":1666},[603,2305,1670],{},[607,2307,1673],{"separator":601},[603,2309,1676],{},[607,2311,1673],{"separator":601},[603,2313,1681],{},[775,2315,2316,2318],{},[607,2317,1686],{"stretchy":1666},[603,2319,1689],{},[611,2321,2322],{"encoding":613},"\\vec n = \\frac{1}{R}(x, y, z)^T",[580,2324,2326,2376],{"className":2325,"ariaHidden":601},[618],[580,2327,2329,2332,2367,2370,2373],{"className":2328},[622],[580,2330],{"className":2331,"style":929},[626],[580,2333,2335],{"className":2334},[631,632],[580,2336,2338],{"className":2337},[636],[580,2339,2341],{"className":2340},[640],[580,2342,2344,2352],{"className":2343,"style":929},[644],[580,2345,2346,2349],{"style":647},[580,2347],{"className":2348,"style":652},[651],[580,2350,914],{"className":2351},[631,656],[580,2353,2354,2357],{"style":647},[580,2355],{"className":2356,"style":652},[651],[580,2358,2360],{"className":2359,"style":958},[667],[580,2361,2363],{"className":2362,"style":673},[672],[675,2364,2365],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,2366],{"d":686},[580,2368],{"className":2369,"style":806},[805],[580,2371,1315],{"className":2372},[810],[580,2374],{"className":2375,"style":806},[805],[580,2377,2379,2383,2455,2458,2461,2464,2467,2470,2473,2476,2479],{"className":2378},[622],[580,2380],{"className":2381,"style":2382},[626],"height:1.1901em;vertical-align:-0.345em;",[580,2384,2386,2389,2452],{"className":2385},[631],[580,2387],{"className":2388},[1756,2125],[580,2390,2392],{"className":2391},[1984],[580,2393,2395,2443],{"className":2394},[636,1378],[580,2396,2398,2440],{"className":2397},[640],[580,2399,2402,2417,2425],{"className":2400,"style":2401},[644],"height:0.8451em;",[580,2403,2405,2408],{"style":2404},"top:-2.655em;",[580,2406],{"className":2407,"style":652},[651],[580,2409,2411],{"className":2410},[851,852,853,854],[580,2412,2414],{"className":2413},[631,854],[580,2415,780],{"className":2416,"style":1841},[631,656,854],[580,2418,2419,2422],{"style":2153},[580,2420],{"className":2421,"style":652},[651],[580,2423],{"className":2424,"style":2161},[2160],[580,2426,2428,2431],{"style":2427},"top:-3.394em;",[580,2429],{"className":2430,"style":652},[651],[580,2432,2434],{"className":2433},[851,852,853,854],[580,2435,2437],{"className":2436},[631,854],[580,2438,1090],{"className":2439},[631,854],[580,2441,1403],{"className":2442},[1402],[580,2444,2446],{"className":2445},[640],[580,2447,2450],{"className":2448,"style":2449},[644],"height:0.345em;",[580,2451],{},[580,2453],{"className":2454},[1784,2125],[580,2456,1667],{"className":2457},[1756],[580,2459,1670],{"className":2460},[631,656],[580,2462,1673],{"className":2463},[1763],[580,2465],{"className":2466,"style":1416},[805],[580,2468,1676],{"className":2469,"style":1770},[631,656],[580,2471,1673],{"className":2472},[1763],[580,2474],{"className":2475,"style":1416},[805],[580,2477,1681],{"className":2478,"style":1780},[631,656],[580,2480,2482,2485],{"className":2481},[1784],[580,2483,1686],{"className":2484},[1784],[580,2486,2488],{"className":2487},[831],[580,2489,2491],{"className":2490},[636],[580,2492,2494],{"className":2493},[640],[580,2495,2497],{"className":2496,"style":1800},[644],[580,2498,2499,2502],{"style":843},[580,2500],{"className":2501,"style":847},[651],[580,2503,2505],{"className":2504},[851,852,853,854],[580,2506,1689],{"className":2507,"style":657},[631,656,854]," und ",[580,2510,2512,2574],{"className":2511},[583],[580,2513,2515],{"className":2514},[587],[589,2516,2517],{"xmlns":591},[593,2518,2519,2571],{},[596,2520,2521,2527,2529,2535,2537,2567,2569],{},[599,2522,2523,2525],{"accent":601},[603,2524,605],{},[607,2526,609],{},[607,2528,1335],{},[599,2530,2531,2533],{"accent":601},[603,2532,914],{},[607,2534,609],{},[607,2536,1315],{},[1984,2538,2539,2565],{},[596,2540,2541,2548,2551,2557,2559],{},[775,2542,2543,2545],{},[603,2544,1670],{},[782,2546,2547],{},"2",[607,2549,2550],{},"+",[775,2552,2553,2555],{},[603,2554,1676],{},[782,2556,2547],{},[607,2558,2550],{},[775,2560,2561,2563],{},[603,2562,1681],{},[782,2564,2547],{},[603,2566,780],{},[607,2568,1315],{},[603,2570,780],{},[611,2572,2573],{"encoding":613},"\\vec F \\cdot \\vec n = \\frac{x^2 + y^2 + z^2}{R} = R",[580,2575,2577,2627,2677,2858],{"className":2576,"ariaHidden":601},[618],[580,2578,2580,2583,2618,2621,2624],{"className":2579},[622],[580,2581],{"className":2582,"style":627},[626],[580,2584,2586],{"className":2585},[631,632],[580,2587,2589],{"className":2588},[636],[580,2590,2592],{"className":2591},[640],[580,2593,2595,2603],{"className":2594,"style":627},[644],[580,2596,2597,2600],{"style":647},[580,2598],{"className":2599,"style":652},[651],[580,2601,605],{"className":2602,"style":657},[631,656],[580,2604,2605,2608],{"style":660},[580,2606],{"className":2607,"style":652},[651],[580,2609,2611],{"className":2610,"style":668},[667],[580,2612,2614],{"className":2613,"style":673},[672],[675,2615,2616],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,2617],{"d":686},[580,2619],{"className":2620,"style":801},[805],[580,2622,1335],{"className":2623},[1582],[580,2625],{"className":2626,"style":801},[805],[580,2628,2630,2633,2668,2671,2674],{"className":2629},[622],[580,2631],{"className":2632,"style":929},[626],[580,2634,2636],{"className":2635},[631,632],[580,2637,2639],{"className":2638},[636],[580,2640,2642],{"className":2641},[640],[580,2643,2645,2653],{"className":2644,"style":929},[644],[580,2646,2647,2650],{"style":647},[580,2648],{"className":2649,"style":652},[651],[580,2651,914],{"className":2652},[631,656],[580,2654,2655,2658],{"style":647},[580,2656],{"className":2657,"style":652},[651],[580,2659,2661],{"className":2660,"style":958},[667],[580,2662,2664],{"className":2663,"style":673},[672],[675,2665,2666],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,2667],{"d":686},[580,2669],{"className":2670,"style":806},[805],[580,2672,1315],{"className":2673},[810],[580,2675],{"className":2676,"style":806},[805],[580,2678,2680,2684,2849,2852,2855],{"className":2679},[622],[580,2681],{"className":2682,"style":2683},[626],"height:1.415em;vertical-align:-0.345em;",[580,2685,2687,2690,2846],{"className":2686},[631],[580,2688],{"className":2689},[1756,2125],[580,2691,2693],{"className":2692},[1984],[580,2694,2696,2838],{"className":2695},[636,1378],[580,2697,2699,2835],{"className":2698},[640],[580,2700,2703,2717,2725],{"className":2701,"style":2702},[644],"height:1.07em;",[580,2704,2705,2708],{"style":2404},[580,2706],{"className":2707,"style":652},[651],[580,2709,2711],{"className":2710},[851,852,853,854],[580,2712,2714],{"className":2713},[631,854],[580,2715,780],{"className":2716,"style":1841},[631,656,854],[580,2718,2719,2722],{"style":2153},[580,2720],{"className":2721,"style":652},[651],[580,2723],{"className":2724,"style":2161},[2160],[580,2726,2728,2731],{"style":2727},"top:-3.4461em;",[580,2729],{"className":2730,"style":652},[651],[580,2732,2734],{"className":2733},[851,852,853,854],[580,2735,2737,2771,2774,2803,2806],{"className":2736},[631,854],[580,2738,2740,2743],{"className":2739},[631,854],[580,2741,1670],{"className":2742},[631,656,854],[580,2744,2746],{"className":2745},[831],[580,2747,2749],{"className":2748},[636],[580,2750,2752],{"className":2751},[640],[580,2753,2756],{"className":2754,"style":2755},[644],"height:0.8913em;",[580,2757,2759,2763],{"style":2758},"top:-2.931em;margin-right:0.0714em;",[580,2760],{"className":2761,"style":2762},[651],"height:2.5em;",[580,2764,2768],{"className":2765},[851,2766,2767,854],"reset-size3","size1",[580,2769,2547],{"className":2770},[631,854],[580,2772,2550],{"className":2773},[1582,854],[580,2775,2777,2780],{"className":2776},[631,854],[580,2778,1676],{"className":2779,"style":1770},[631,656,854],[580,2781,2783],{"className":2782},[831],[580,2784,2786],{"className":2785},[636],[580,2787,2789],{"className":2788},[640],[580,2790,2792],{"className":2791,"style":2755},[644],[580,2793,2794,2797],{"style":2758},[580,2795],{"className":2796,"style":2762},[651],[580,2798,2800],{"className":2799},[851,2766,2767,854],[580,2801,2547],{"className":2802},[631,854],[580,2804,2550],{"className":2805},[1582,854],[580,2807,2809,2812],{"className":2808},[631,854],[580,2810,1681],{"className":2811,"style":1780},[631,656,854],[580,2813,2815],{"className":2814},[831],[580,2816,2818],{"className":2817},[636],[580,2819,2821],{"className":2820},[640],[580,2822,2824],{"className":2823,"style":2755},[644],[580,2825,2826,2829],{"style":2758},[580,2827],{"className":2828,"style":2762},[651],[580,2830,2832],{"className":2831},[851,2766,2767,854],[580,2833,2547],{"className":2834},[631,854],[580,2836,1403],{"className":2837},[1402],[580,2839,2841],{"className":2840},[640],[580,2842,2844],{"className":2843,"style":2449},[644],[580,2845],{},[580,2847],{"className":2848},[1784,2125],[580,2850],{"className":2851,"style":806},[805],[580,2853,1315],{"className":2854},[810],[580,2856],{"className":2857,"style":806},[805],[580,2859,2861,2864],{"className":2860},[622],[580,2862],{"className":2863,"style":1057},[626],[580,2865,780],{"className":2866,"style":1841},[631,656],". Der Fluss ist ",[580,2869,2871,2909],{"className":2870},[583],[580,2872,2874],{"className":2873},[587],[589,2875,2876],{"xmlns":591},[593,2877,2878,2906],{},[596,2879,2880,2882,2884,2886,2888,2894,2896,2898,2900],{},[603,2881,780],{},[607,2883,1335],{},[782,2885,1988],{},[603,2887,1993],{},[775,2889,2890,2892],{},[603,2891,780],{},[782,2893,2547],{},[607,2895,1315],{},[782,2897,1988],{},[603,2899,1993],{},[775,2901,2902,2904],{},[603,2903,780],{},[782,2905,784],{},[611,2907,2908],{"encoding":613},"R \\cdot 4\\pi R^2 = 4\\pi R^3",[580,2910,2912,2930,2980],{"className":2911,"ariaHidden":601},[618],[580,2913,2915,2918,2921,2924,2927],{"className":2914},[622],[580,2916],{"className":2917,"style":1057},[626],[580,2919,780],{"className":2920,"style":1841},[631,656],[580,2922],{"className":2923,"style":801},[805],[580,2925,1335],{"className":2926},[1582],[580,2928],{"className":2929,"style":801},[805],[580,2931,2933,2936,2939,2942,2971,2974,2977],{"className":2932},[622],[580,2934],{"className":2935,"style":820},[626],[580,2937,1988],{"className":2938},[631],[580,2940,1993],{"className":2941,"style":1770},[631,656],[580,2943,2945,2948],{"className":2944},[631],[580,2946,780],{"className":2947,"style":1841},[631,656],[580,2949,2951],{"className":2950},[831],[580,2952,2954],{"className":2953},[636],[580,2955,2957],{"className":2956},[640],[580,2958,2960],{"className":2959,"style":820},[644],[580,2961,2962,2965],{"style":843},[580,2963],{"className":2964,"style":847},[651],[580,2966,2968],{"className":2967},[851,852,853,854],[580,2969,2547],{"className":2970},[631,854],[580,2972],{"className":2973,"style":806},[805],[580,2975,1315],{"className":2976},[810],[580,2978],{"className":2979,"style":806},[805],[580,2981,2983,2986,2989,2992],{"className":2982},[622],[580,2984],{"className":2985,"style":820},[626],[580,2987,1988],{"className":2988},[631],[580,2990,1993],{"className":2991,"style":1770},[631,656],[580,2993,2995,2998],{"className":2994},[631],[580,2996,780],{"className":2997,"style":1841},[631,656],[580,2999,3001],{"className":3000},[831],[580,3002,3004],{"className":3003},[636],[580,3005,3007],{"className":3006},[640],[580,3008,3010],{"className":3009,"style":820},[644],[580,3011,3012,3015],{"style":843},[580,3013],{"className":3014,"style":847},[651],[580,3016,3018],{"className":3017},[851,852,853,854],[580,3019,784],{"className":3020},[631,854],". Für ",[580,3023,3025,3043],{"className":3024},[583],[580,3026,3028],{"className":3027},[587],[589,3029,3030],{"xmlns":591},[593,3031,3032,3040],{},[596,3033,3034,3036,3038],{},[603,3035,780],{},[607,3037,1315],{},[782,3039,2547],{},[611,3041,3042],{"encoding":613},"R = 2",[580,3044,3046,3064],{"className":3045,"ariaHidden":601},[618],[580,3047,3049,3052,3055,3058,3061],{"className":3048},[622],[580,3050],{"className":3051,"style":1057},[626],[580,3053,780],{"className":3054,"style":1841},[631,656],[580,3056],{"className":3057,"style":806},[805],[580,3059,1315],{"className":3060},[810],[580,3062],{"className":3063,"style":806},[805],[580,3065,3067,3070],{"className":3066},[622],[580,3068],{"className":3069,"style":1940},[626],[580,3071,2547],{"className":3072},[631]," ergibt das ",[580,3075,3077,3100],{"className":3076},[583],[580,3078,3080],{"className":3079},[587],[589,3081,3082],{"xmlns":591},[593,3083,3084,3097],{},[596,3085,3086,3089,3091,3094],{},[782,3087,3088],{},"32",[603,3090,1993],{},[607,3092,3093],{},"≈",[782,3095,3096],{},"100,53",[611,3098,3099],{"encoding":613},"32\\pi \\approx 100{,}53",[580,3101,3103,3124],{"className":3102,"ariaHidden":601},[618],[580,3104,3106,3109,3112,3115,3118,3121],{"className":3105},[622],[580,3107],{"className":3108,"style":1940},[626],[580,3110,3088],{"className":3111},[631],[580,3113,1993],{"className":3114,"style":1770},[631,656],[580,3116],{"className":3117,"style":806},[805],[580,3119,3093],{"className":3120},[810],[580,3122],{"className":3123,"style":806},[805],[580,3125,3127,3131,3135,3141],{"className":3126},[622],[580,3128],{"className":3129,"style":3130},[626],"height:0.8389em;vertical-align:-0.1944em;",[580,3132,3134],{"className":3133},[631],"100",[580,3136,3138],{"className":3137},[631],[580,3139,1673],{"className":3140},[1763],[580,3142,3144],{"className":3143},[631],"53",[565,3146,1643,3147,3401,3402,1842,3488,3649],{},[580,3148,3150,3205],{"className":3149},[583],[580,3151,3153],{"className":3152},[587],[589,3154,3155],{"xmlns":591},[593,3156,3157,3202],{},[596,3158,3159,3165,3167,3169,3175,3177,3180,3186,3188,3190,3196],{},[599,3160,3161,3163],{"accent":601},[603,3162,605],{},[607,3164,609],{},[607,3166,1315],{},[607,3168,1667],{"stretchy":1666},[775,3170,3171,3173],{},[603,3172,1670],{},[782,3174,2547],{},[607,3176,1673],{"separator":601},[1304,3178,3179],{}," ",[775,3181,3182,3184],{},[603,3183,1676],{},[782,3185,2547],{},[607,3187,1673],{"separator":601},[1304,3189,3179],{},[775,3191,3192,3194],{},[603,3193,1681],{},[782,3195,2547],{},[775,3197,3198,3200],{},[607,3199,1686],{"stretchy":1666},[603,3201,1689],{},[611,3203,3204],{"encoding":613},"\\vec F = (x^2,\\ y^2,\\ z^2)^T",[580,3206,3208,3258],{"className":3207,"ariaHidden":601},[618],[580,3209,3211,3214,3249,3252,3255],{"className":3210},[622],[580,3212],{"className":3213,"style":627},[626],[580,3215,3217],{"className":3216},[631,632],[580,3218,3220],{"className":3219},[636],[580,3221,3223],{"className":3222},[640],[580,3224,3226,3234],{"className":3225,"style":627},[644],[580,3227,3228,3231],{"style":647},[580,3229],{"className":3230,"style":652},[651],[580,3232,605],{"className":3233,"style":657},[631,656],[580,3235,3236,3239],{"style":660},[580,3237],{"className":3238,"style":652},[651],[580,3240,3242],{"className":3241,"style":668},[667],[580,3243,3245],{"className":3244,"style":673},[672],[675,3246,3247],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,3248],{"d":686},[580,3250],{"className":3251,"style":806},[805],[580,3253,1315],{"className":3254},[810],[580,3256],{"className":3257,"style":806},[805],[580,3259,3261,3264,3267,3296,3299,3302,3305,3334,3337,3340,3343,3372],{"className":3260},[622],[580,3262],{"className":3263,"style":1752},[626],[580,3265,1667],{"className":3266},[1756],[580,3268,3270,3273],{"className":3269},[631],[580,3271,1670],{"className":3272},[631,656],[580,3274,3276],{"className":3275},[831],[580,3277,3279],{"className":3278},[636],[580,3280,3282],{"className":3281},[640],[580,3283,3285],{"className":3284,"style":820},[644],[580,3286,3287,3290],{"style":843},[580,3288],{"className":3289,"style":847},[651],[580,3291,3293],{"className":3292},[851,852,853,854],[580,3294,2547],{"className":3295},[631,854],[580,3297,1673],{"className":3298},[1763],[580,3300,3179],{"className":3301},[805],[580,3303],{"className":3304,"style":1416},[805],[580,3306,3308,3311],{"className":3307},[631],[580,3309,1676],{"className":3310,"style":1770},[631,656],[580,3312,3314],{"className":3313},[831],[580,3315,3317],{"className":3316},[636],[580,3318,3320],{"className":3319},[640],[580,3321,3323],{"className":3322,"style":820},[644],[580,3324,3325,3328],{"style":843},[580,3326],{"className":3327,"style":847},[651],[580,3329,3331],{"className":3330},[851,852,853,854],[580,3332,2547],{"className":3333},[631,854],[580,3335,1673],{"className":3336},[1763],[580,3338,3179],{"className":3339},[805],[580,3341],{"className":3342,"style":1416},[805],[580,3344,3346,3349],{"className":3345},[631],[580,3347,1681],{"className":3348,"style":1780},[631,656],[580,3350,3352],{"className":3351},[831],[580,3353,3355],{"className":3354},[636],[580,3356,3358],{"className":3357},[640],[580,3359,3361],{"className":3360,"style":820},[644],[580,3362,3363,3366],{"style":843},[580,3364],{"className":3365,"style":847},[651],[580,3367,3369],{"className":3368},[851,852,853,854],[580,3370,2547],{"className":3371},[631,854],[580,3373,3375,3378],{"className":3374},[1784],[580,3376,1686],{"className":3377},[1784],[580,3379,3381],{"className":3380},[831],[580,3382,3384],{"className":3383},[636],[580,3385,3387],{"className":3386},[640],[580,3388,3390],{"className":3389,"style":1800},[644],[580,3391,3392,3395],{"style":843},[580,3393],{"className":3394,"style":847},[651],[580,3396,3398],{"className":3397},[851,852,853,854],[580,3399,1689],{"className":3400,"style":657},[631,656,854]," und den Einheitswürfel ",[580,3403,3405,3434],{"className":3404},[583],[580,3406,3408],{"className":3407},[587],[589,3409,3410],{"xmlns":591},[593,3411,3412,3431],{},[596,3413,3414,3417,3420,3422,3424],{},[607,3415,3416],{"stretchy":1666},"[",[782,3418,3419],{},"0",[607,3421,1673],{"separator":601},[782,3423,1090],{},[775,3425,3426,3429],{},[607,3427,3428],{"stretchy":1666},"]",[782,3430,784],{},[611,3432,3433],{"encoding":613},"[0, 1]^3",[580,3435,3437],{"className":3436,"ariaHidden":601},[618],[580,3438,3440,3444,3447,3450,3453,3456,3459],{"className":3439},[622],[580,3441],{"className":3442,"style":3443},[626],"height:1.0641em;vertical-align:-0.25em;",[580,3445,3416],{"className":3446},[1756],[580,3448,3419],{"className":3449},[631],[580,3451,1673],{"className":3452},[1763],[580,3454],{"className":3455,"style":1416},[805],[580,3457,1090],{"className":3458},[631],[580,3460,3462,3465],{"className":3461},[1784],[580,3463,3428],{"className":3464},[1784],[580,3466,3468],{"className":3467},[831],[580,3469,3471],{"className":3470},[636],[580,3472,3474],{"className":3473},[640],[580,3475,3477],{"className":3476,"style":820},[644],[580,3478,3479,3482],{"style":843},[580,3480],{"className":3481,"style":847},[651],[580,3483,3485],{"className":3484},[851,852,853,854],[580,3486,784],{"className":3487},[631,854],[580,3489,3491,3531],{"className":3490},[583],[580,3492,3494],{"className":3493},[587],[589,3495,3496],{"xmlns":591},[593,3497,3498,3528],{},[596,3499,3500,3502,3504,3510,3512,3514,3516,3518,3520,3522,3524,3526],{},[603,3501,1293],{"mathvariant":873},[607,3503,1296],{},[599,3505,3506,3508],{"accent":601},[603,3507,605],{},[607,3509,609],{},[607,3511,1315],{},[782,3513,2547],{},[607,3515,1667],{"stretchy":1666},[603,3517,1670],{},[607,3519,2550],{},[603,3521,1676],{},[607,3523,2550],{},[603,3525,1681],{},[607,3527,1686],{"stretchy":1666},[611,3529,3530],{"encoding":613},"\\operatorname{div} \\vec F = 2(x + y + z)",[580,3532,3534,3593,3618,3637],{"className":3533,"ariaHidden":601},[618],[580,3535,3537,3540,3546,3549,3584,3587,3590],{"className":3536},[622],[580,3538],{"className":3539,"style":627},[626],[580,3541,3543],{"className":3542},[1365],[580,3544,1293],{"className":3545,"style":1424},[631,1423],[580,3547],{"className":3548,"style":1416},[805],[580,3550,3552],{"className":3551},[631,632],[580,3553,3555],{"className":3554},[636],[580,3556,3558],{"className":3557},[640],[580,3559,3561,3569],{"className":3560,"style":627},[644],[580,3562,3563,3566],{"style":647},[580,3564],{"className":3565,"style":652},[651],[580,3567,605],{"className":3568,"style":657},[631,656],[580,3570,3571,3574],{"style":660},[580,3572],{"className":3573,"style":652},[651],[580,3575,3577],{"className":3576,"style":668},[667],[580,3578,3580],{"className":3579,"style":673},[672],[675,3581,3582],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,3583],{"d":686},[580,3585],{"className":3586,"style":806},[805],[580,3588,1315],{"className":3589},[810],[580,3591],{"className":3592,"style":806},[805],[580,3594,3596,3600,3603,3606,3609,3612,3615],{"className":3595},[622],[580,3597],{"className":3598,"style":3599},[626],"height:1em;vertical-align:-0.25em;",[580,3601,2547],{"className":3602},[631],[580,3604,1667],{"className":3605},[1756],[580,3607,1670],{"className":3608},[631,656],[580,3610],{"className":3611,"style":801},[805],[580,3613,2550],{"className":3614},[1582],[580,3616],{"className":3617,"style":801},[805],[580,3619,3621,3625,3628,3631,3634],{"className":3620},[622],[580,3622],{"className":3623,"style":3624},[626],"height:0.7778em;vertical-align:-0.1944em;",[580,3626,1676],{"className":3627,"style":1770},[631,656],[580,3629],{"className":3630,"style":801},[805],[580,3632,2550],{"className":3633},[1582],[580,3635],{"className":3636,"style":801},[805],[580,3638,3640,3643,3646],{"className":3639},[622],[580,3641],{"className":3642,"style":3599},[626],[580,3644,1681],{"className":3645,"style":1780},[631,656],[580,3647,1686],{"className":3648},[1784]," und",[580,3651,3653],{"className":3652},[1948],[580,3654,3656,3726],{"className":3655},[583],[580,3657,3659],{"className":3658},[587],[589,3660,3661],{"xmlns":591,"display":1957},[593,3662,3663,3723],{},[596,3664,3665,3685,3687,3689,3691,3693,3695,3697,3699,3701,3703,3705,3707,3709,3711,3713,3719,3721],{},[1283,3666,3667,3669],{},[607,3668,1966],{},[596,3670,3671,3673,3675,3677,3679],{},[607,3672,3416],{"stretchy":1666},[782,3674,3419],{},[607,3676,1673],{"separator":601},[782,3678,1090],{},[775,3680,3681,3683],{},[607,3682,3428],{"stretchy":1666},[782,3684,784],{},[782,3686,2547],{},[607,3688,1667],{"stretchy":1666},[603,3690,1670],{},[607,3692,2550],{},[603,3694,1676],{},[607,3696,2550],{},[603,3698,1681],{},[607,3700,1686],{"stretchy":1666},[1304,3702,1306],{},[603,3704,1309],{},[603,3706,770],{},[607,3708,1315],{},[782,3710,2547],{},[607,3712,1335],{},[1984,3714,3715,3717],{},[782,3716,784],{},[782,3718,2547],{},[607,3720,1315],{},[782,3722,784],{},[611,3724,3725],{"encoding":613},"\\iiint_{[0,1]^3} 2(x + y + z)\\, dV = 2 \\cdot \\frac{3}{2} = 3",[580,3727,3729,3842,3860,3890,3908,3985],{"className":3728,"ariaHidden":601},[618],[580,3730,3732,3736,3821,3824,3827,3830,3833,3836,3839],{"className":3731},[622],[580,3733],{"className":3734,"style":3735},[626],"height:2.4467em;vertical-align:-1.0867em;",[580,3737,3739,3742],{"className":3738},[1365],[580,3740,1966],{"className":3741,"style":2032},[1365,1369,2031],[580,3743,3745],{"className":3744},[831],[580,3746,3748,3812],{"className":3747},[636,1378],[580,3749,3751,3809],{"className":3750},[640],[580,3752,3755],{"className":3753,"style":3754},[644],"height:-0.3867em;",[580,3756,3757,3760],{"style":2048},[580,3758],{"className":3759,"style":847},[651],[580,3761,3763],{"className":3762},[851,852,853,854],[580,3764,3766,3769,3772,3775,3778],{"className":3765},[631,854],[580,3767,3416],{"className":3768},[1756,854],[580,3770,3419],{"className":3771},[631,854],[580,3773,1673],{"className":3774},[1763,854],[580,3776,1090],{"className":3777},[631,854],[580,3779,3781,3784],{"className":3780},[1784,854],[580,3782,3428],{"className":3783},[1784,854],[580,3785,3787],{"className":3786},[831],[580,3788,3790],{"className":3789},[636],[580,3791,3793],{"className":3792},[640],[580,3794,3797],{"className":3795,"style":3796},[644],"height:0.7463em;",[580,3798,3800,3803],{"style":3799},"top:-2.786em;margin-right:0.0714em;",[580,3801],{"className":3802,"style":2762},[651],[580,3804,3806],{"className":3805},[851,2766,2767,854],[580,3807,784],{"className":3808},[631,854],[580,3810,1403],{"className":3811},[1402],[580,3813,3815],{"className":3814},[640],[580,3816,3819],{"className":3817,"style":3818},[644],"height:1.0867em;",[580,3820],{},[580,3822],{"className":3823,"style":1416},[805],[580,3825,2547],{"className":3826},[631],[580,3828,1667],{"className":3829},[1756],[580,3831,1670],{"className":3832},[631,656],[580,3834],{"className":3835,"style":801},[805],[580,3837,2550],{"className":3838},[1582],[580,3840],{"className":3841,"style":801},[805],[580,3843,3845,3848,3851,3854,3857],{"className":3844},[622],[580,3846],{"className":3847,"style":3624},[626],[580,3849,1676],{"className":3850,"style":1770},[631,656],[580,3852],{"className":3853,"style":801},[805],[580,3855,2550],{"className":3856},[1582],[580,3858],{"className":3859,"style":801},[805],[580,3861,3863,3866,3869,3872,3875,3878,3881,3884,3887],{"className":3862},[622],[580,3864],{"className":3865,"style":3599},[626],[580,3867,1681],{"className":3868,"style":1780},[631,656],[580,3870,1686],{"className":3871},[1784],[580,3873],{"className":3874,"style":1416},[805],[580,3876,1309],{"className":3877},[631,656],[580,3879,770],{"className":3880,"style":801},[631,656],[580,3882],{"className":3883,"style":806},[805],[580,3885,1315],{"className":3886},[810],[580,3888],{"className":3889,"style":806},[805],[580,3891,3893,3896,3899,3902,3905],{"className":3892},[622],[580,3894],{"className":3895,"style":1940},[626],[580,3897,2547],{"className":3898},[631],[580,3900],{"className":3901,"style":801},[805],[580,3903,1335],{"className":3904},[1582],[580,3906],{"className":3907,"style":801},[805],[580,3909,3911,3914,3976,3979,3982],{"className":3910},[622],[580,3912],{"className":3913,"style":2118},[626],[580,3915,3917,3920,3973],{"className":3916},[631],[580,3918],{"className":3919},[1756,2125],[580,3921,3923],{"className":3922},[1984],[580,3924,3926,3965],{"className":3925},[636,1378],[580,3927,3929,3962],{"className":3928},[640],[580,3930,3932,3943,3951],{"className":3931,"style":2138},[644],[580,3933,3934,3937],{"style":2141},[580,3935],{"className":3936,"style":652},[651],[580,3938,3940],{"className":3939},[631],[580,3941,2547],{"className":3942},[631],[580,3944,3945,3948],{"style":2153},[580,3946],{"className":3947,"style":652},[651],[580,3949],{"className":3950,"style":2161},[2160],[580,3952,3953,3956],{"style":2164},[580,3954],{"className":3955,"style":652},[651],[580,3957,3959],{"className":3958},[631],[580,3960,784],{"className":3961},[631],[580,3963,1403],{"className":3964},[1402],[580,3966,3968],{"className":3967},[640],[580,3969,3971],{"className":3970,"style":2183},[644],[580,3972],{},[580,3974],{"className":3975},[1784,2125],[580,3977],{"className":3978,"style":806},[805],[580,3980,1315],{"className":3981},[810],[580,3983],{"className":3984,"style":806},[805],[580,3986,3988,3991],{"className":3987},[622],[580,3989],{"className":3990,"style":1940},[626],[580,3992,784],{"className":3993},[631],[565,3995,3996,3997,1842,4049,2508,4202,4347,4348,4376,4377,1842,4428,4632,4633,1636],{},"Direkt: Auf der Seite ",[580,3998,4000,4018],{"className":3999},[583],[580,4001,4003],{"className":4002},[587],[589,4004,4005],{"xmlns":591},[593,4006,4007,4015],{},[596,4008,4009,4011,4013],{},[603,4010,1670],{},[607,4012,1315],{},[782,4014,1090],{},[611,4016,4017],{"encoding":613},"x = 1",[580,4019,4021,4040],{"className":4020,"ariaHidden":601},[618],[580,4022,4024,4028,4031,4034,4037],{"className":4023},[622],[580,4025],{"className":4026,"style":4027},[626],"height:0.4306em;",[580,4029,1670],{"className":4030},[631,656],[580,4032],{"className":4033,"style":806},[805],[580,4035,1315],{"className":4036},[810],[580,4038],{"className":4039,"style":806},[805],[580,4041,4043,4046],{"className":4042},[622],[580,4044],{"className":4045,"style":1940},[626],[580,4047,1090],{"className":4048},[631],[580,4050,4052,4090],{"className":4051},[583],[580,4053,4055],{"className":4054},[587],[589,4056,4057],{"xmlns":591},[593,4058,4059,4087],{},[596,4060,4061,4067,4069,4071,4073,4075,4077,4079,4081],{},[599,4062,4063,4065],{"accent":601},[603,4064,914],{},[607,4066,609],{},[607,4068,1315],{},[607,4070,1667],{"stretchy":1666},[782,4072,1090],{},[607,4074,1673],{"separator":601},[782,4076,3419],{},[607,4078,1673],{"separator":601},[782,4080,3419],{},[775,4082,4083,4085],{},[607,4084,1686],{"stretchy":1666},[603,4086,1689],{},[611,4088,4089],{"encoding":613},"\\vec n = (1, 0, 0)^T",[580,4091,4093,4143],{"className":4092,"ariaHidden":601},[618],[580,4094,4096,4099,4134,4137,4140],{"className":4095},[622],[580,4097],{"className":4098,"style":929},[626],[580,4100,4102],{"className":4101},[631,632],[580,4103,4105],{"className":4104},[636],[580,4106,4108],{"className":4107},[640],[580,4109,4111,4119],{"className":4110,"style":929},[644],[580,4112,4113,4116],{"style":647},[580,4114],{"className":4115,"style":652},[651],[580,4117,914],{"className":4118},[631,656],[580,4120,4121,4124],{"style":647},[580,4122],{"className":4123,"style":652},[651],[580,4125,4127],{"className":4126,"style":958},[667],[580,4128,4130],{"className":4129,"style":673},[672],[675,4131,4132],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,4133],{"d":686},[580,4135],{"className":4136,"style":806},[805],[580,4138,1315],{"className":4139},[810],[580,4141],{"className":4142,"style":806},[805],[580,4144,4146,4149,4152,4155,4158,4161,4164,4167,4170,4173],{"className":4145},[622],[580,4147],{"className":4148,"style":1752},[626],[580,4150,1667],{"className":4151},[1756],[580,4153,1090],{"className":4154},[631],[580,4156,1673],{"className":4157},[1763],[580,4159],{"className":4160,"style":1416},[805],[580,4162,3419],{"className":4163},[631],[580,4165,1673],{"className":4166},[1763],[580,4168],{"className":4169,"style":1416},[805],[580,4171,3419],{"className":4172},[631],[580,4174,4176,4179],{"className":4175},[1784],[580,4177,1686],{"className":4178},[1784],[580,4180,4182],{"className":4181},[831],[580,4183,4185],{"className":4184},[636],[580,4186,4188],{"className":4187},[640],[580,4189,4191],{"className":4190,"style":1800},[644],[580,4192,4193,4196],{"style":843},[580,4194],{"className":4195,"style":847},[651],[580,4197,4199],{"className":4198},[851,852,853,854],[580,4200,1689],{"className":4201,"style":657},[631,656,854],[580,4203,4205,4235],{"className":4204},[583],[580,4206,4208],{"className":4207},[587],[589,4209,4210],{"xmlns":591},[593,4211,4212,4232],{},[596,4213,4214,4220,4222,4228,4230],{},[599,4215,4216,4218],{"accent":601},[603,4217,605],{},[607,4219,609],{},[607,4221,1335],{},[599,4223,4224,4226],{"accent":601},[603,4225,914],{},[607,4227,609],{},[607,4229,1315],{},[782,4231,1090],{},[611,4233,4234],{"encoding":613},"\\vec F \\cdot \\vec n = 1",[580,4236,4238,4288,4338],{"className":4237,"ariaHidden":601},[618],[580,4239,4241,4244,4279,4282,4285],{"className":4240},[622],[580,4242],{"className":4243,"style":627},[626],[580,4245,4247],{"className":4246},[631,632],[580,4248,4250],{"className":4249},[636],[580,4251,4253],{"className":4252},[640],[580,4254,4256,4264],{"className":4255,"style":627},[644],[580,4257,4258,4261],{"style":647},[580,4259],{"className":4260,"style":652},[651],[580,4262,605],{"className":4263,"style":657},[631,656],[580,4265,4266,4269],{"style":660},[580,4267],{"className":4268,"style":652},[651],[580,4270,4272],{"className":4271,"style":668},[667],[580,4273,4275],{"className":4274,"style":673},[672],[675,4276,4277],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,4278],{"d":686},[580,4280],{"className":4281,"style":801},[805],[580,4283,1335],{"className":4284},[1582],[580,4286],{"className":4287,"style":801},[805],[580,4289,4291,4294,4329,4332,4335],{"className":4290},[622],[580,4292],{"className":4293,"style":929},[626],[580,4295,4297],{"className":4296},[631,632],[580,4298,4300],{"className":4299},[636],[580,4301,4303],{"className":4302},[640],[580,4304,4306,4314],{"className":4305,"style":929},[644],[580,4307,4308,4311],{"style":647},[580,4309],{"className":4310,"style":652},[651],[580,4312,914],{"className":4313},[631,656],[580,4315,4316,4319],{"style":647},[580,4317],{"className":4318,"style":652},[651],[580,4320,4322],{"className":4321,"style":958},[667],[580,4323,4325],{"className":4324,"style":673},[672],[675,4326,4327],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,4328],{"d":686},[580,4330],{"className":4331,"style":806},[805],[580,4333,1315],{"className":4334},[810],[580,4336],{"className":4337,"style":806},[805],[580,4339,4341,4344],{"className":4340},[622],[580,4342],{"className":4343,"style":1940},[626],[580,4345,1090],{"className":4346},[631],", der Fluss dort also ",[580,4349,4351,4364],{"className":4350},[583],[580,4352,4354],{"className":4353},[587],[589,4355,4356],{"xmlns":591},[593,4357,4358,4362],{},[596,4359,4360],{},[782,4361,1090],{},[611,4363,1090],{"encoding":613},[580,4365,4367],{"className":4366,"ariaHidden":601},[618],[580,4368,4370,4373],{"className":4369},[622],[580,4371],{"className":4372,"style":1940},[626],[580,4374,1090],{"className":4375},[631],". Auf ",[580,4378,4380,4398],{"className":4379},[583],[580,4381,4383],{"className":4382},[587],[589,4384,4385],{"xmlns":591},[593,4386,4387,4395],{},[596,4388,4389,4391,4393],{},[603,4390,1670],{},[607,4392,1315],{},[782,4394,3419],{},[611,4396,4397],{"encoding":613},"x = 0",[580,4399,4401,4419],{"className":4400,"ariaHidden":601},[618],[580,4402,4404,4407,4410,4413,4416],{"className":4403},[622],[580,4405],{"className":4406,"style":4027},[626],[580,4408,1670],{"className":4409},[631,656],[580,4411],{"className":4412,"style":806},[805],[580,4414,1315],{"className":4415},[810],[580,4417],{"className":4418,"style":806},[805],[580,4420,4422,4425],{"className":4421},[622],[580,4423],{"className":4424,"style":1940},[626],[580,4426,3419],{"className":4427},[631],[580,4429,4431,4472],{"className":4430},[583],[580,4432,4434],{"className":4433},[587],[589,4435,4436],{"xmlns":591},[593,4437,4438,4469],{},[596,4439,4440,4446,4448,4454,4456,4459,4465,4467],{},[599,4441,4442,4444],{"accent":601},[603,4443,605],{},[607,4445,609],{},[607,4447,1335],{},[599,4449,4450,4452],{"accent":601},[603,4451,914],{},[607,4453,609],{},[607,4455,1315],{},[607,4457,4458],{},"−",[775,4460,4461,4463],{},[603,4462,1670],{},[782,4464,2547],{},[607,4466,1315],{},[782,4468,3419],{},[611,4470,4471],{"encoding":613},"\\vec F \\cdot \\vec n = -x^2 = 0",[580,4473,4475,4525,4575,4623],{"className":4474,"ariaHidden":601},[618],[580,4476,4478,4481,4516,4519,4522],{"className":4477},[622],[580,4479],{"className":4480,"style":627},[626],[580,4482,4484],{"className":4483},[631,632],[580,4485,4487],{"className":4486},[636],[580,4488,4490],{"className":4489},[640],[580,4491,4493,4501],{"className":4492,"style":627},[644],[580,4494,4495,4498],{"style":647},[580,4496],{"className":4497,"style":652},[651],[580,4499,605],{"className":4500,"style":657},[631,656],[580,4502,4503,4506],{"style":660},[580,4504],{"className":4505,"style":652},[651],[580,4507,4509],{"className":4508,"style":668},[667],[580,4510,4512],{"className":4511,"style":673},[672],[675,4513,4514],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,4515],{"d":686},[580,4517],{"className":4518,"style":801},[805],[580,4520,1335],{"className":4521},[1582],[580,4523],{"className":4524,"style":801},[805],[580,4526,4528,4531,4566,4569,4572],{"className":4527},[622],[580,4529],{"className":4530,"style":929},[626],[580,4532,4534],{"className":4533},[631,632],[580,4535,4537],{"className":4536},[636],[580,4538,4540],{"className":4539},[640],[580,4541,4543,4551],{"className":4542,"style":929},[644],[580,4544,4545,4548],{"style":647},[580,4546],{"className":4547,"style":652},[651],[580,4549,914],{"className":4550},[631,656],[580,4552,4553,4556],{"style":647},[580,4554],{"className":4555,"style":652},[651],[580,4557,4559],{"className":4558,"style":958},[667],[580,4560,4562],{"className":4561,"style":673},[672],[675,4563,4564],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,4565],{"d":686},[580,4567],{"className":4568,"style":806},[805],[580,4570,1315],{"className":4571},[810],[580,4573],{"className":4574,"style":806},[805],[580,4576,4578,4582,4585,4614,4617,4620],{"className":4577},[622],[580,4579],{"className":4580,"style":4581},[626],"height:0.8974em;vertical-align:-0.0833em;",[580,4583,4458],{"className":4584},[631],[580,4586,4588,4591],{"className":4587},[631],[580,4589,1670],{"className":4590},[631,656],[580,4592,4594],{"className":4593},[831],[580,4595,4597],{"className":4596},[636],[580,4598,4600],{"className":4599},[640],[580,4601,4603],{"className":4602,"style":820},[644],[580,4604,4605,4608],{"style":843},[580,4606],{"className":4607,"style":847},[651],[580,4609,4611],{"className":4610},[851,852,853,854],[580,4612,2547],{"className":4613},[631,854],[580,4615],{"className":4616,"style":806},[805],[580,4618,1315],{"className":4619},[810],[580,4621],{"className":4622,"style":806},[805],[580,4624,4626,4629],{"className":4625},[622],[580,4627],{"className":4628,"style":1940},[626],[580,4630,3419],{"className":4631},[631],". Mit den anderen Richtungen ergibt sich zusammen ",[580,4634,4636,4666],{"className":4635},[583],[580,4637,4639],{"className":4638},[587],[589,4640,4641],{"xmlns":591},[593,4642,4643,4663],{},[596,4644,4645,4647,4649,4651,4653,4655,4657,4659,4661],{},[782,4646,784],{},[607,4648,1335],{},[607,4650,1667],{"stretchy":1666},[782,4652,1090],{},[607,4654,4458],{},[782,4656,3419],{},[607,4658,1686],{"stretchy":1666},[607,4660,1315],{},[782,4662,784],{},[611,4664,4665],{"encoding":613},"3 \\cdot (1 - 0) = 3",[580,4667,4669,4687,4708,4729],{"className":4668,"ariaHidden":601},[618],[580,4670,4672,4675,4678,4681,4684],{"className":4671},[622],[580,4673],{"className":4674,"style":1940},[626],[580,4676,784],{"className":4677},[631],[580,4679],{"className":4680,"style":801},[805],[580,4682,1335],{"className":4683},[1582],[580,4685],{"className":4686,"style":801},[805],[580,4688,4690,4693,4696,4699,4702,4705],{"className":4689},[622],[580,4691],{"className":4692,"style":3599},[626],[580,4694,1667],{"className":4695},[1756],[580,4697,1090],{"className":4698},[631],[580,4700],{"className":4701,"style":801},[805],[580,4703,4458],{"className":4704},[1582],[580,4706],{"className":4707,"style":801},[805],[580,4709,4711,4714,4717,4720,4723,4726],{"className":4710},[622],[580,4712],{"className":4713,"style":3599},[626],[580,4715,3419],{"className":4716},[631],[580,4718,1686],{"className":4719},[1784],[580,4721],{"className":4722,"style":806},[805],[580,4724,1315],{"className":4725},[810],[580,4727],{"className":4728,"style":806},[805],[580,4730,4732,4735],{"className":4731},[622],[580,4733],{"className":4734,"style":1940},[626],[580,4736,784],{"className":4737},[631],[560,4739,4741],{"id":4740},"typische-fehler","Typische Fehler",[1189,4743,4744,4747,4750],{},[1192,4745,4746],{},"Die Normale nach innen richten. Dann ändert sich das Vorzeichen des Flusses.",[1192,4748,4749],{},"Den Satz auf eine offene Fläche anwenden, z.B. eine Halbkugel ohne Boden. Fehlende Teile der Oberfläche müssen ergänzt und ihr Fluss wieder abgezogen werden.",[1192,4751,4752,4753,4817,4818,5096,5097,5125,5126,1636],{},"Bei einer Singularität im Inneren rechnen, als wäre ",[580,4754,4756,4773],{"className":4755},[583],[580,4757,4759],{"className":4758},[587],[589,4760,4761],{"xmlns":591},[593,4762,4763,4771],{},[596,4764,4765],{},[599,4766,4767,4769],{"accent":601},[603,4768,605],{},[607,4770,609],{},[611,4772,614],{"encoding":613},[580,4774,4776],{"className":4775,"ariaHidden":601},[618],[580,4777,4779,4782],{"className":4778},[622],[580,4780],{"className":4781,"style":627},[626],[580,4783,4785],{"className":4784},[631,632],[580,4786,4788],{"className":4787},[636],[580,4789,4791],{"className":4790},[640],[580,4792,4794,4802],{"className":4793,"style":627},[644],[580,4795,4796,4799],{"style":647},[580,4797],{"className":4798,"style":652},[651],[580,4800,605],{"className":4801,"style":657},[631,656],[580,4803,4804,4807],{"style":660},[580,4805],{"className":4806,"style":652},[651],[580,4808,4810],{"className":4809,"style":668},[667],[580,4811,4813],{"className":4812,"style":673},[672],[675,4814,4815],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,4816],{"d":686}," überall glatt. Für ",[580,4819,4821,4867],{"className":4820},[583],[580,4822,4824],{"className":4823},[587],[589,4825,4826],{"xmlns":591},[593,4827,4828,4864],{},[596,4829,4830,4836,4838],{},[599,4831,4832,4834],{"accent":601},[603,4833,605],{},[607,4835,609],{},[607,4837,1315],{},[1984,4839,4840,4847],{},[599,4841,4842,4845],{"accent":601},[603,4843,4844],{},"r",[607,4846,609],{},[596,4848,4849,4852,4858],{},[603,4850,4851],{"mathvariant":873},"∣",[599,4853,4854,4856],{"accent":601},[603,4855,4844],{},[607,4857,609],{},[775,4859,4860,4862],{},[603,4861,4851],{"mathvariant":873},[782,4863,784],{},[611,4865,4866],{"encoding":613},"\\vec F = \\frac{\\vec r}{|\\vec r|^3}",[580,4868,4870,4920],{"className":4869,"ariaHidden":601},[618],[580,4871,4873,4876,4911,4914,4917],{"className":4872},[622],[580,4874],{"className":4875,"style":627},[626],[580,4877,4879],{"className":4878},[631,632],[580,4880,4882],{"className":4881},[636],[580,4883,4885],{"className":4884},[640],[580,4886,4888,4896],{"className":4887,"style":627},[644],[580,4889,4890,4893],{"style":647},[580,4891],{"className":4892,"style":652},[651],[580,4894,605],{"className":4895,"style":657},[631,656],[580,4897,4898,4901],{"style":660},[580,4899],{"className":4900,"style":652},[651],[580,4902,4904],{"className":4903,"style":668},[667],[580,4905,4907],{"className":4906,"style":673},[672],[675,4908,4909],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,4910],{"d":686},[580,4912],{"className":4913,"style":806},[805],[580,4915,1315],{"className":4916},[810],[580,4918],{"className":4919,"style":806},[805],[580,4921,4923,4927],{"className":4922},[622],[580,4924],{"className":4925,"style":4926},[626],"height:1.4138em;vertical-align:-0.52em;",[580,4928,4930,4933,5093],{"className":4929},[631],[580,4931],{"className":4932},[1756,2125],[580,4934,4936],{"className":4935},[1984],[580,4937,4939,5084],{"className":4938},[636,1378],[580,4940,4942,5081],{"className":4941},[640],[580,4943,4946,5027,5035],{"className":4944,"style":4945},[644],"height:0.8938em;",[580,4947,4948,4951],{"style":2404},[580,4949],{"className":4950,"style":652},[651],[580,4952,4954],{"className":4953},[851,852,853,854],[580,4955,4957,4960,4998],{"className":4956},[631,854],[580,4958,4851],{"className":4959},[631,854],[580,4961,4963],{"className":4962},[631,632,854],[580,4964,4966],{"className":4965},[636],[580,4967,4969],{"className":4968},[640],[580,4970,4972,4982],{"className":4971,"style":929},[644],[580,4973,4975,4979],{"style":4974},"top:-2.714em;",[580,4976],{"className":4977,"style":4978},[651],"height:2.714em;",[580,4980,4844],{"className":4981,"style":1398},[631,656,854],[580,4983,4984,4987],{"style":4974},[580,4985],{"className":4986,"style":4978},[651],[580,4988,4991],{"className":4989,"style":4990},[667],"left:-0.1799em;",[580,4992,4994],{"className":4993,"style":673},[672,854],[675,4995,4996],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,4997],{"d":686},[580,4999,5001,5004],{"className":5000},[631,854],[580,5002,4851],{"className":5003},[631,854],[580,5005,5007],{"className":5006},[831],[580,5008,5010],{"className":5009},[636],[580,5011,5013],{"className":5012},[640],[580,5014,5016],{"className":5015,"style":3796},[644],[580,5017,5018,5021],{"style":3799},[580,5019],{"className":5020,"style":2762},[651],[580,5022,5024],{"className":5023},[851,2766,2767,854],[580,5025,784],{"className":5026},[631,854],[580,5028,5029,5032],{"style":2153},[580,5030],{"className":5031,"style":652},[651],[580,5033],{"className":5034,"style":2161},[2160],[580,5036,5037,5040],{"style":2427},[580,5038],{"className":5039,"style":652},[651],[580,5041,5043],{"className":5042},[851,852,853,854],[580,5044,5046],{"className":5045},[631,854],[580,5047,5049],{"className":5048},[631,632,854],[580,5050,5052],{"className":5051},[636],[580,5053,5055],{"className":5054},[640],[580,5056,5058,5066],{"className":5057,"style":929},[644],[580,5059,5060,5063],{"style":4974},[580,5061],{"className":5062,"style":4978},[651],[580,5064,4844],{"className":5065,"style":1398},[631,656,854],[580,5067,5068,5071],{"style":4974},[580,5069],{"className":5070,"style":4978},[651],[580,5072,5074],{"className":5073,"style":4990},[667],[580,5075,5077],{"className":5076,"style":673},[672,854],[675,5078,5079],{"xmlns":677,"width":678,"height":679,"style":680,"viewBox":681,"preserveAspectRatio":682},[684,5080],{"d":686},[580,5082,1403],{"className":5083},[1402],[580,5085,5087],{"className":5086},[640],[580,5088,5091],{"className":5089,"style":5090},[644],"height:0.52em;",[580,5092],{},[580,5094],{"className":5095},[1784,2125]," ist die Divergenz außerhalb des Ursprungs ",[580,5098,5100,5113],{"className":5099},[583],[580,5101,5103],{"className":5102},[587],[589,5104,5105],{"xmlns":591},[593,5106,5107,5111],{},[596,5108,5109],{},[782,5110,3419],{},[611,5112,3419],{"encoding":613},[580,5114,5116],{"className":5115,"ariaHidden":601},[618],[580,5117,5119,5122],{"className":5118},[622],[580,5120],{"className":5121,"style":1940},[626],[580,5123,3419],{"className":5124},[631],", der Fluss durch jede Kugel um den Ursprung aber ",[580,5127,5129,5145],{"className":5128},[583],[580,5130,5132],{"className":5131},[587],[589,5133,5134],{"xmlns":591},[593,5135,5136,5142],{},[596,5137,5138,5140],{},[782,5139,1988],{},[603,5141,1993],{},[611,5143,5144],{"encoding":613},"4\\pi",[580,5146,5148],{"className":5147,"ariaHidden":601},[618],[580,5149,5151,5154,5157],{"className":5150},[622],[580,5152],{"className":5153,"style":1940},[626],[580,5155,1988],{"className":5156},[631],[580,5158,1993],{"className":5159,"style":1770},[631,656],{"title":5161,"searchDepth":5162,"depth":5162,"links":5163},"",2,[5164,5165,5166],{"id":562,"depth":5162,"text":563},{"id":1639,"depth":5162,"text":1640},{"id":4740,"depth":5162,"text":4741},[5168,5171,5173,5176,5178],{"lhs":5169,"rhs":5170},"3 * 4\u002F3*pi*R^3","4*pi*R^3",{"lhs":5172,"rhs":5170},"R * 4*pi*R^2",{"lhs":5174,"rhs":5175},"round(4*pi*2^3, 2)","100.53",{"lhs":5177,"rhs":784},"2 * 3\u002F2",{"lhs":5179,"rhs":784},"3 * (1^2 - 0^2)","V \\text{ beschränkt},\\ \\vec{n} \\text{ äußere Normale},\\ {\\vec{F} \\in C^1}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">beschränkt\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>\u003Cmover accent=\"true\">\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{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:0.714em;\">\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\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">äußere\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">Normale\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>\u003Cmover accent=\"true\">\u003Cmi>F\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi>C\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">{\\vec{F} \\in C^1}\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:1.0054em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\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 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>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\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 mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","divergence-theorem","\\iiint_V \\operatorname{div} \\vec{F}\\, dV = \\oiint_{\\partial V} \\vec{F} \\cdot \\vec{n}\\, dS","\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>\u003Cmi>V\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmi 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