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Das Volumen ist die Summe all dieser Kreisflächen, also ihr Integral.",[564,923,924,925,969,970,998],{},"Weil ",[568,926,928,948],{"className":927},[571],[568,929,931],{"className":930},[575],[577,932,933],{"xmlns":579},[581,934,935,945],{},[584,936,937,939,941,943],{},[587,938,589],{},[760,940,763],{"stretchy":762},[587,942,691],{},[760,944,768],{"stretchy":762},[591,946,947],{"encoding":593},"f(x)",[568,949,951],{"className":950,"ariaHidden":598},[597],[568,952,954,957,960,963,966],{"className":953},[602],[568,955],{"className":956,"style":783},[606],[568,958,589],{"className":959,"style":613},[611,612],[568,961,763],{"className":962},[793],[568,964,691],{"className":965},[611,612],[568,967,768],{"className":968},[800]," quadriert wird, spielt es keine Rolle, ob der Graph über oder unter der ",[568,971,973,986],{"className":972},[571],[568,974,976],{"className":975},[575],[577,977,978],{"xmlns":579},[581,979,980,984],{},[584,981,982],{},[587,983,691],{},[591,985,691],{"encoding":593},[568,987,989],{"className":988,"ariaHidden":598},[597],[568,990,992,995],{"className":991},[602],[568,993],{"className":994,"style":641},[606],[568,996,691],{"className":997},[611,612],"-Achse liegt.",[564,1000,1001,1002,645,1030,1060,1061,1141,1142,1433],{},"Liegt zwischen zwei Graphen ",[568,1003,1005,1018],{"className":1004},[571],[568,1006,1008],{"className":1007},[575],[577,1009,1010],{"xmlns":579},[581,1011,1012,1016],{},[584,1013,1014],{},[587,1015,589],{},[591,1017,589],{"encoding":593},[568,1019,1021],{"className":1020,"ariaHidden":598},[597],[568,1022,1024,1027],{"className":1023},[602],[568,1025],{"className":1026,"style":607},[606],[568,1028,589],{"className":1029,"style":613},[611,612],[568,1031,1033,1047],{"className":1032},[571],[568,1034,1036],{"className":1035},[575],[577,1037,1038],{"xmlns":579},[581,1039,1040,1045],{},[584,1041,1042],{},[587,1043,1044],{},"g",[591,1046,1044],{"encoding":593},[568,1048,1050],{"className":1049,"ariaHidden":598},[597],[568,1051,1053,1057],{"className":1052},[602],[568,1054],{"className":1055,"style":1056},[606],"height:0.625em;vertical-align:-0.1944em;",[568,1058,1044],{"className":1059,"style":856},[611,612]," mit ",[568,1062,1064,1088],{"className":1063},[571],[568,1065,1067],{"className":1066},[575],[577,1068,1069],{"xmlns":579},[581,1070,1071,1085],{},[584,1072,1073,1076,1079,1081,1083],{},[837,1074,1075],{},"0",[760,1077,1078],{},"≤",[587,1080,1044],{},[760,1082,1078],{},[587,1084,589],{},[591,1086,1087],{"encoding":593},"0 \\leq g \\leq f",[568,1089,1091,1113,1132],{"className":1090,"ariaHidden":598},[597],[568,1092,1094,1098,1101,1106,1110],{"className":1093},[602],[568,1095],{"className":1096,"style":1097},[606],"height:0.7804em;vertical-align:-0.136em;",[568,1099,1075],{"className":1100},[611],[568,1102],{"className":1103,"style":1105},[1104],"mspace","margin-right:0.2778em;",[568,1107,1078],{"className":1108},[1109],"mrel",[568,1111],{"className":1112,"style":1105},[1104],[568,1114,1116,1120,1123,1126,1129],{"className":1115},[602],[568,1117],{"className":1118,"style":1119},[606],"height:0.8304em;vertical-align:-0.1944em;",[568,1121,1044],{"className":1122,"style":856},[611,612],[568,1124],{"className":1125,"style":1105},[1104],[568,1127,1078],{"className":1128},[1109],[568,1130],{"className":1131,"style":1105},[1104],[568,1133,1135,1138],{"className":1134},[602],[568,1136],{"className":1137,"style":607},[606],[568,1139,589],{"className":1140,"style":613},[611,612]," ein Hohlraum, rechnet man ",[568,1143,1145,1215],{"className":1144},[571],[568,1146,1148],{"className":1147},[575],[577,1149,1150],{"xmlns":579},[581,1151,1152,1212],{},[584,1153,1154,1157,1160,1162,1172,1174,1176,1178,1180,1186,1189,1191,1193,1195,1201,1203,1207,1210],{},[587,1155,1156],{},"V",[760,1158,1159],{},"=",[587,1161,819],{},[1163,1164,1165,1168,1170],"msubsup",{},[760,1166,1167],{},"∫",[587,1169,629],{},[587,1171,660],{},[760,1173,763],{"fence":762,"stretchy":598,"minsize":822,"maxsize":822},[587,1175,589],{},[760,1177,763],{"stretchy":762},[587,1179,691],{},[832,1181,1182,1184],{},[760,1183,768],{"stretchy":762},[837,1185,839],{},[760,1187,1188],{},"−",[587,1190,1044],{},[760,1192,763],{"stretchy":762},[587,1194,691],{},[832,1196,1197,1199],{},[760,1198,768],{"stretchy":762},[837,1200,839],{},[760,1202,768],{"fence":762,"stretchy":598,"minsize":822,"maxsize":822},[1204,1205,1206],"mtext",{}," ",[587,1208,1209],{},"d",[587,1211,691],{},[591,1213,1214],{"encoding":593},"V = \\pi \\int_a^b \\big(f(x)^2 - g(x)^2\\big)\\,dx",[568,1216,1218,1238,1373],{"className":1217,"ariaHidden":598},[597],[568,1219,1221,1225,1229,1232,1235],{"className":1220},[602],[568,1222],{"className":1223,"style":1224},[606],"height:0.6833em;",[568,1226,1156],{"className":1227,"style":1228},[611,612],"margin-right:0.2222em;",[568,1230],{"className":1231,"style":1105},[1104],[568,1233,1159],{"className":1234},[1109],[568,1236],{"className":1237,"style":1105},[1104],[568,1239,1241,1245,1248,1252,1314,1317,1323,1326,1329,1332,1363,1366,1370],{"className":1240},[602],[568,1242],{"className":1243,"style":1244},[606],"height:1.3998em;vertical-align:-0.3558em;",[568,1246,819],{"className":1247,"style":856},[611,612],[568,1249],{"className":1250,"style":1251},[1104],"margin-right:0.1667em;",[568,1253,1256,1262],{"className":1254},[1255],"mop",[568,1257,1167],{"className":1258,"style":1261},[1255,1259,1260],"op-symbol","small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[568,1263,1265],{"className":1264},[889],[568,1266,1269,1305],{"className":1267},[893,1268],"vlist-t2",[568,1270,1272,1300],{"className":1271},[897],[568,1273,1276,1288],{"className":1274,"style":1275},[901],"height:1.044em;",[568,1277,1279,1282],{"style":1278},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[568,1280],{"className":1281,"style":910},[909],[568,1283,1285],{"className":1284},[914,915,916,917],[568,1286,629],{"className":1287},[611,612,917],[568,1289,1291,1294],{"style":1290},"top:-3.2579em;margin-right:0.05em;",[568,1292],{"className":1293,"style":910},[909],[568,1295,1297],{"className":1296},[914,915,916,917],[568,1298,660],{"className":1299},[611,612,917],[568,1301,1304],{"className":1302},[1303],"vlist-s","​",[568,1306,1308],{"className":1307},[897],[568,1309,1312],{"className":1310,"style":1311},[901],"height:0.3558em;",[568,1313],{},[568,1315],{"className":1316,"style":1251},[1104],[568,1318,1320],{"className":1319},[611],[568,1321,763],{"className":1322},[863,864],[568,1324,589],{"className":1325,"style":613},[611,612],[568,1327,763],{"className":1328},[793],[568,1330,691],{"className":1331},[611,612],[568,1333,1335,1338],{"className":1334},[800],[568,1336,768],{"className":1337},[800],[568,1339,1341],{"className":1340},[889],[568,1342,1344],{"className":1343},[893],[568,1345,1347],{"className":1346},[897],[568,1348,1351],{"className":1349,"style":1350},[901],"height:0.8141em;",[568,1352,1354,1357],{"style":1353},"top:-3.063em;margin-right:0.05em;",[568,1355],{"className":1356,"style":910},[909],[568,1358,1360],{"className":1359},[914,915,916,917],[568,1361,839],{"className":1362},[611,917],[568,1364],{"className":1365,"style":1228},[1104],[568,1367,1188],{"className":1368},[1369],"mbin",[568,1371],{"className":1372,"style":1228},[1104],[568,1374,1376,1380,1383,1386,1389,1418,1424,1427,1430],{"className":1375},[602],[568,1377],{"className":1378,"style":1379},[606],"height:1.2em;vertical-align:-0.35em;",[568,1381,1044],{"className":1382,"style":856},[611,612],[568,1384,763],{"className":1385},[793],[568,1387,691],{"className":1388},[611,612],[568,1390,1392,1395],{"className":1391},[800],[568,1393,768],{"className":1394},[800],[568,1396,1398],{"className":1397},[889],[568,1399,1401],{"className":1400},[893],[568,1402,1404],{"className":1403},[897],[568,1405,1407],{"className":1406,"style":1350},[901],[568,1408,1409,1412],{"style":1353},[568,1410],{"className":1411,"style":910},[909],[568,1413,1415],{"className":1414},[914,915,916,917],[568,1416,839],{"className":1417},[611,917],[568,1419,1421],{"className":1420},[611],[568,1422,768],{"className":1423},[863,864],[568,1425],{"className":1426,"style":1251},[1104],[568,1428,1209],{"className":1429},[611,612],[568,1431,691],{"className":1432},[611,612],".",[559,1435,1437],{"id":1436},"herleitung","Herleitung",[564,1439,1440,1441,1476,1477,1600,1601,1634,1635,1664],{},"Man zerlegt den Körper in dünne Scheiben der Dicke ",[568,1442,1444,1461],{"className":1443},[571],[568,1445,1447],{"className":1446},[575],[577,1448,1449],{"xmlns":579},[581,1450,1451,1458],{},[584,1452,1453,1456],{},[587,1454,1455],{"mathvariant":755},"Δ",[587,1457,691],{},[591,1459,1460],{"encoding":593},"\\Delta x",[568,1462,1464],{"className":1463,"ariaHidden":598},[597],[568,1465,1467,1470,1473],{"className":1466},[602],[568,1468],{"className":1469,"style":1224},[606],[568,1471,1455],{"className":1472},[611],[568,1474,691],{"className":1475},[611,612],". Jede Scheibe ist näherungsweise ein Zylinder mit Volumen ",[568,1478,1480,1517],{"className":1479},[571],[568,1481,1483],{"className":1482},[575],[577,1484,1485],{"xmlns":579},[581,1486,1487,1514],{},[584,1488,1489,1491,1493,1495,1497,1499,1501,1507,1510,1512],{},[587,1490,819],{},[760,1492,763],{"fence":762,"stretchy":598,"minsize":822,"maxsize":822},[587,1494,589],{},[760,1496,763],{"stretchy":762},[587,1498,691],{},[760,1500,768],{"stretchy":762},[832,1502,1503,1505],{},[760,1504,768],{"fence":762,"stretchy":598,"minsize":822,"maxsize":822},[837,1506,839],{},[760,1508,1509],{},"⋅",[587,1511,1455],{"mathvariant":755},[587,1513,691],{},[591,1515,1516],{"encoding":593},"\\pi \\big(f(x)\\big)^2 \\cdot \\Delta x",[568,1518,1520,1588],{"className":1519,"ariaHidden":598},[597],[568,1521,1523,1526,1529,1535,1538,1541,1544,1547,1579,1582,1585],{"className":1522},[602],[568,1524],{"className":1525,"style":852},[606],[568,1527,819],{"className":1528,"style":856},[611,612],[568,1530,1532],{"className":1531},[611],[568,1533,763],{"className":1534},[863,864],[568,1536,589],{"className":1537,"style":613},[611,612],[568,1539,763],{"className":1540},[793],[568,1542,691],{"className":1543},[611,612],[568,1545,768],{"className":1546},[800],[568,1548,1550,1556],{"className":1549},[611],[568,1551,1553],{"className":1552},[611],[568,1554,768],{"className":1555},[863,864],[568,1557,1559],{"className":1558},[889],[568,1560,1562],{"className":1561},[893],[568,1563,1565],{"className":1564},[897],[568,1566,1568],{"className":1567,"style":902},[901],[568,1569,1570,1573],{"style":905},[568,1571],{"className":1572,"style":910},[909],[568,1574,1576],{"className":1575},[914,915,916,917],[568,1577,839],{"className":1578},[611,917],[568,1580],{"className":1581,"style":1228},[1104],[568,1583,1509],{"className":1584},[1369],[568,1586],{"className":1587,"style":1228},[1104],[568,1589,1591,1594,1597],{"className":1590},[602],[568,1592],{"className":1593,"style":1224},[606],[568,1595,1455],{"className":1596},[611],[568,1598,691],{"className":1599},[611,612],". Summiert man die Scheiben und lässt ",[568,1602,1604,1619],{"className":1603},[571],[568,1605,1607],{"className":1606},[575],[577,1608,1609],{"xmlns":579},[581,1610,1611,1617],{},[584,1612,1613,1615],{},[587,1614,1455],{"mathvariant":755},[587,1616,691],{},[591,1618,1460],{"encoding":593},[568,1620,1622],{"className":1621,"ariaHidden":598},[597],[568,1623,1625,1628,1631],{"className":1624},[602],[568,1626],{"className":1627,"style":1224},[606],[568,1629,1455],{"className":1630},[611],[568,1632,691],{"className":1633},[611,612]," gegen ",[568,1636,1638,1651],{"className":1637},[571],[568,1639,1641],{"className":1640},[575],[577,1642,1643],{"xmlns":579},[581,1644,1645,1649],{},[584,1646,1647],{},[837,1648,1075],{},[591,1650,1075],{"encoding":593},[568,1652,1654],{"className":1653,"ariaHidden":598},[597],[568,1655,1657,1661],{"className":1656},[602],[568,1658],{"className":1659,"style":1660},[606],"height:0.6444em;",[568,1662,1075],{"className":1663},[611]," gehen, erhält man das Integral.",[559,1666,1668],{"id":1667},"beispiele","Beispiele",[564,1670,1671,1674,1675,1834,1835,645,1863,1891,1892,1920,1921,1949],{},[708,1672,1673],{},"Kegel",": Die Gerade ",[568,1676,1678,1713],{"className":1677},[571],[568,1679,1681],{"className":1680},[575],[577,1682,1683],{"xmlns":579},[581,1684,1685,1710],{},[584,1686,1687,1689,1691,1693,1695,1697,1706,1708],{},[587,1688,589],{},[760,1690,763],{"stretchy":762},[587,1692,691],{},[760,1694,768],{"stretchy":762},[760,1696,1159],{},[1698,1699,1700,1703],"mfrac",{},[587,1701,1702],{},"r",[587,1704,1705],{},"h",[1204,1707,1206],{},[587,1709,691],{},[591,1711,1712],{"encoding":593},"f(x) = \\frac{r}{h}\\,x",[568,1714,1716,1743],{"className":1715,"ariaHidden":598},[597],[568,1717,1719,1722,1725,1728,1731,1734,1737,1740],{"className":1718},[602],[568,1720],{"className":1721,"style":783},[606],[568,1723,589],{"className":1724,"style":613},[611,612],[568,1726,763],{"className":1727},[793],[568,1729,691],{"className":1730},[611,612],[568,1732,768],{"className":1733},[800],[568,1735],{"className":1736,"style":1105},[1104],[568,1738,1159],{"className":1739},[1109],[568,1741],{"className":1742,"style":1105},[1104],[568,1744,1746,1750,1828,1831],{"className":1745},[602],[568,1747],{"className":1748,"style":1749},[606],"height:1.0404em;vertical-align:-0.345em;",[568,1751,1753,1757,1825],{"className":1752},[611],[568,1754],{"className":1755},[793,1756],"nulldelimiter",[568,1758,1760],{"className":1759},[1698],[568,1761,1763,1816],{"className":1762},[893,1268],[568,1764,1766,1813],{"className":1765},[897],[568,1767,1770,1786,1797],{"className":1768,"style":1769},[901],"height:0.6954em;",[568,1771,1773,1777],{"style":1772},"top:-2.655em;",[568,1774],{"className":1775,"style":1776},[909],"height:3em;",[568,1778,1780],{"className":1779},[914,915,916,917],[568,1781,1783],{"className":1782},[611,917],[568,1784,1705],{"className":1785},[611,612,917],[568,1787,1789,1792],{"style":1788},"top:-3.23em;",[568,1790],{"className":1791,"style":1776},[909],[568,1793],{"className":1794,"style":1796},[1795],"frac-line","border-bottom-width:0.04em;",[568,1798,1800,1803],{"style":1799},"top:-3.394em;",[568,1801],{"className":1802,"style":1776},[909],[568,1804,1806],{"className":1805},[914,915,916,917],[568,1807,1809],{"className":1808},[611,917],[568,1810,1702],{"className":1811,"style":1812},[611,612,917],"margin-right:0.0278em;",[568,1814,1304],{"className":1815},[1303],[568,1817,1819],{"className":1818},[897],[568,1820,1823],{"className":1821,"style":1822},[901],"height:0.345em;",[568,1824],{},[568,1826],{"className":1827},[800,1756],[568,1829],{"className":1830,"style":1251},[1104],[568,1832,691],{"className":1833},[611,612]," rotiert zwischen ",[568,1836,1838,1851],{"className":1837},[571],[568,1839,1841],{"className":1840},[575],[577,1842,1843],{"xmlns":579},[581,1844,1845,1849],{},[584,1846,1847],{},[837,1848,1075],{},[591,1850,1075],{"encoding":593},[568,1852,1854],{"className":1853,"ariaHidden":598},[597],[568,1855,1857,1860],{"className":1856},[602],[568,1858],{"className":1859,"style":1660},[606],[568,1861,1075],{"className":1862},[611],[568,1864,1866,1879],{"className":1865},[571],[568,1867,1869],{"className":1868},[575],[577,1870,1871],{"xmlns":579},[581,1872,1873,1877],{},[584,1874,1875],{},[587,1876,1705],{},[591,1878,1705],{"encoding":593},[568,1880,1882],{"className":1881,"ariaHidden":598},[597],[568,1883,1885,1888],{"className":1884},[602],[568,1886],{"className":1887,"style":672},[606],[568,1889,1705],{"className":1890},[611,612]," und erzeugt einen Kegel mit Radius ",[568,1893,1895,1908],{"className":1894},[571],[568,1896,1898],{"className":1897},[575],[577,1899,1900],{"xmlns":579},[581,1901,1902,1906],{},[584,1903,1904],{},[587,1905,1702],{},[591,1907,1702],{"encoding":593},[568,1909,1911],{"className":1910,"ariaHidden":598},[597],[568,1912,1914,1917],{"className":1913},[602],[568,1915],{"className":1916,"style":641},[606],[568,1918,1702],{"className":1919,"style":1812},[611,612]," und Höhe ",[568,1922,1924,1937],{"className":1923},[571],[568,1925,1927],{"className":1926},[575],[577,1928,1929],{"xmlns":579},[581,1930,1931,1935],{},[584,1932,1933],{},[587,1934,1705],{},[591,1936,1705],{"encoding":593},[568,1938,1940],{"className":1939,"ariaHidden":598},[597],[568,1941,1943,1946],{"className":1942},[602],[568,1944],{"className":1945,"style":672},[606],[568,1947,1705],{"className":1948},[611,612],":",[568,1951,1954],{"className":1952},[1953],"katex-display",[568,1955,1957,2066],{"className":1956},[571],[568,1958,1960],{"className":1959},[575],[577,1961,1963],{"xmlns":579,"display":1962},"block",[581,1964,1965,2063],{},[584,1966,1967,1969,1971,1973,1981,1995,1997,2003,2005,2007,2009,2011,2013,2015,2029,2031,2042,2044,2051,2053,2055,2061],{},[587,1968,1156],{},[760,1970,1159],{},[587,1972,819],{},[1163,1974,1975,1977,1979],{},[760,1976,1167],{},[837,1978,1075],{},[587,1980,1705],{},[1698,1982,1983,1989],{},[832,1984,1985,1987],{},[587,1986,1702],{},[837,1988,839],{},[832,1990,1991,1993],{},[587,1992,1705],{},[837,1994,839],{},[1204,1996,1206],{},[832,1998,1999,2001],{},[587,2000,691],{},[837,2002,839],{},[1204,2004,1206],{},[587,2006,1209],{},[587,2008,691],{},[760,2010,1159],{},[587,2012,819],{},[1204,2014,1206],{},[1698,2016,2017,2023],{},[832,2018,2019,2021],{},[587,2020,1702],{},[837,2022,839],{},[832,2024,2025,2027],{},[587,2026,1705],{},[837,2028,839],{},[760,2030,1509],{},[1698,2032,2033,2040],{},[832,2034,2035,2037],{},[587,2036,1705],{},[837,2038,2039],{},"3",[837,2041,2039],{},[760,2043,1159],{},[1698,2045,2046,2049],{},[837,2047,2048],{},"1",[837,2050,2039],{},[1204,2052,1206],{},[587,2054,819],{},[832,2056,2057,2059],{},[587,2058,1702],{},[837,2060,839],{},[587,2062,1705],{},[591,2064,2065],{"encoding":593},"V = \\pi \\int_0^h \\frac{r^2}{h^2}\\,x^2\\,dx = \\pi\\,\\frac{r^2}{h^2} \\cdot \\frac{h^3}{3} = \\frac{1}{3}\\,\\pi r^2 h",[568,2067,2069,2087,2332,2468,2571],{"className":2068,"ariaHidden":598},[597],[568,2070,2072,2075,2078,2081,2084],{"className":2071},[602],[568,2073],{"className":2074,"style":1224},[606],[568,2076,1156],{"className":2077,"style":1228},[611,612],[568,2079],{"className":2080,"style":1105},[1104],[568,2082,1159],{"className":2083},[1109],[568,2085],{"className":2086,"style":1105},[1104],[568,2088,2090,2094,2097,2100,2157,2160,2280,2283,2314,2317,2320,2323,2326,2329],{"className":2089},[602],[568,2091],{"className":2092,"style":2093},[606],"height:2.511em;vertical-align:-0.9119em;",[568,2095,819],{"className":2096,"style":856},[611,612],[568,2098],{"className":2099,"style":1251},[1104],[568,2101,2103,2108],{"className":2102},[1255],[568,2104,1167],{"className":2105,"style":2107},[1255,1259,2106],"large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[568,2109,2111],{"className":2110},[889],[568,2112,2114,2148],{"className":2113},[893,1268],[568,2115,2117,2145],{"className":2116},[897],[568,2118,2121,2133],{"className":2119,"style":2120},[901],"height:1.599em;",[568,2122,2124,2127],{"style":2123},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[568,2125],{"className":2126,"style":910},[909],[568,2128,2130],{"className":2129},[914,915,916,917],[568,2131,1075],{"className":2132},[611,917],[568,2134,2136,2139],{"style":2135},"top:-3.8129em;margin-right:0.05em;",[568,2137],{"className":2138,"style":910},[909],[568,2140,2142],{"className":2141},[914,915,916,917],[568,2143,1705],{"className":2144},[611,612,917],[568,2146,1304],{"className":2147},[1303],[568,2149,2151],{"className":2150},[897],[568,2152,2155],{"className":2153,"style":2154},[901],"height:0.9119em;",[568,2156],{},[568,2158],{"className":2159,"style":1251},[1104],[568,2161,2163,2166,2277],{"className":2162},[611],[568,2164],{"className":2165},[793,1756],[568,2167,2169],{"className":2168},[1698],[568,2170,2172,2268],{"className":2171},[893,1268],[568,2173,2175,2265],{"className":2174},[897],[568,2176,2179,2219,2227],{"className":2177,"style":2178},[901],"height:1.4911em;",[568,2180,2182,2185],{"style":2181},"top:-2.314em;",[568,2183],{"className":2184,"style":1776},[909],[568,2186,2188],{"className":2187},[611],[568,2189,2191,2194],{"className":2190},[611],[568,2192,1705],{"className":2193},[611,612],[568,2195,2197],{"className":2196},[889],[568,2198,2200],{"className":2199},[893],[568,2201,2203],{"className":2202},[897],[568,2204,2207],{"className":2205,"style":2206},[901],"height:0.7401em;",[568,2208,2210,2213],{"style":2209},"top:-2.989em;margin-right:0.05em;",[568,2211],{"className":2212,"style":910},[909],[568,2214,2216],{"className":2215},[914,915,916,917],[568,2217,839],{"className":2218},[611,917],[568,2220,2221,2224],{"style":1788},[568,2222],{"className":2223,"style":1776},[909],[568,2225],{"className":2226,"style":1796},[1795],[568,2228,2230,2233],{"style":2229},"top:-3.677em;",[568,2231],{"className":2232,"style":1776},[909],[568,2234,2236],{"className":2235},[611],[568,2237,2239,2242],{"className":2238},[611],[568,2240,1702],{"className":2241,"style":1812},[611,612],[568,2243,2245],{"className":2244},[889],[568,2246,2248],{"className":2247},[893],[568,2249,2251],{"className":2250},[897],[568,2252,2254],{"className":2253,"style":1350},[901],[568,2255,2256,2259],{"style":1353},[568,2257],{"className":2258,"style":910},[909],[568,2260,2262],{"className":2261},[914,915,916,917],[568,2263,839],{"className":2264},[611,917],[568,2266,1304],{"className":2267},[1303],[568,2269,2271],{"className":2270},[897],[568,2272,2275],{"className":2273,"style":2274},[901],"height:0.686em;",[568,2276],{},[568,2278],{"className":2279},[800,1756],[568,2281],{"className":2282,"style":1251},[1104],[568,2284,2286,2289],{"className":2285},[611],[568,2287,691],{"className":2288},[611,612],[568,2290,2292],{"className":2291},[889],[568,2293,2295],{"className":2294},[893],[568,2296,2298],{"className":2297},[897],[568,2299,2302],{"className":2300,"style":2301},[901],"height:0.8641em;",[568,2303,2305,2308],{"style":2304},"top:-3.113em;margin-right:0.05em;",[568,2306],{"className":2307,"style":910},[909],[568,2309,2311],{"className":2310},[914,915,916,917],[568,2312,839],{"className":2313},[611,917],[568,2315],{"className":2316,"style":1251},[1104],[568,2318,1209],{"className":2319},[611,612],[568,2321,691],{"className":2322},[611,612],[568,2324],{"className":2325,"style":1105},[1104],[568,2327,1159],{"className":2328},[1109],[568,2330],{"className":2331,"style":1105},[1104],[568,2333,2335,2339,2342,2345,2459,2462,2465],{"className":2334},[602],[568,2336],{"className":2337,"style":2338},[606],"height:2.1771em;vertical-align:-0.686em;",[568,2340,819],{"className":2341,"style":856},[611,612],[568,2343],{"className":2344,"style":1251},[1104],[568,2346,2348,2351,2456],{"className":2347},[611],[568,2349],{"className":2350},[793,1756],[568,2352,2354],{"className":2353},[1698],[568,2355,2357,2448],{"className":2356},[893,1268],[568,2358,2360,2445],{"className":2359},[897],[568,2361,2363,2400,2408],{"className":2362,"style":2178},[901],[568,2364,2365,2368],{"style":2181},[568,2366],{"className":2367,"style":1776},[909],[568,2369,2371],{"className":2370},[611],[568,2372,2374,2377],{"className":2373},[611],[568,2375,1705],{"className":2376},[611,612],[568,2378,2380],{"className":2379},[889],[568,2381,2383],{"className":2382},[893],[568,2384,2386],{"className":2385},[897],[568,2387,2389],{"className":2388,"style":2206},[901],[568,2390,2391,2394],{"style":2209},[568,2392],{"className":2393,"style":910},[909],[568,2395,2397],{"className":2396},[914,915,916,917],[568,2398,839],{"className":2399},[611,917],[568,2401,2402,2405],{"style":1788},[568,2403],{"className":2404,"style":1776},[909],[568,2406],{"className":2407,"style":1796},[1795],[568,2409,2410,2413],{"style":2229},[568,2411],{"className":2412,"style":1776},[909],[568,2414,2416],{"className":2415},[611],[568,2417,2419,2422],{"className":2418},[611],[568,2420,1702],{"className":2421,"style":1812},[611,612],[568,2423,2425],{"className":2424},[889],[568,2426,2428],{"className":2427},[893],[568,2429,2431],{"className":2430},[897],[568,2432,2434],{"className":2433,"style":1350},[901],[568,2435,2436,2439],{"style":1353},[568,2437],{"className":2438,"style":910},[909],[568,2440,2442],{"className":2441},[914,915,916,917],[568,2443,839],{"className":2444},[611,917],[568,2446,1304],{"className":2447},[1303],[568,2449,2451],{"className":2450},[897],[568,2452,2454],{"className":2453,"style":2274},[901],[568,2455],{},[568,2457],{"className":2458},[800,1756],[568,2460],{"className":2461,"style":1228},[1104],[568,2463,1509],{"className":2464},[1369],[568,2466],{"className":2467,"style":1228},[1104],[568,2469,2471,2474,2562,2565,2568],{"className":2470},[602],[568,2472],{"className":2473,"style":2338},[606],[568,2475,2477,2480,2559],{"className":2476},[611],[568,2478],{"className":2479},[793,1756],[568,2481,2483],{"className":2482},[1698],[568,2484,2486,2551],{"className":2485},[893,1268],[568,2487,2489,2548],{"className":2488},[897],[568,2490,2492,2503,2511],{"className":2491,"style":2178},[901],[568,2493,2494,2497],{"style":2181},[568,2495],{"className":2496,"style":1776},[909],[568,2498,2500],{"className":2499},[611],[568,2501,2039],{"className":2502},[611],[568,2504,2505,2508],{"style":1788},[568,2506],{"className":2507,"style":1776},[909],[568,2509],{"className":2510,"style":1796},[1795],[568,2512,2513,2516],{"style":2229},[568,2514],{"className":2515,"style":1776},[909],[568,2517,2519],{"className":2518},[611],[568,2520,2522,2525],{"className":2521},[611],[568,2523,1705],{"className":2524},[611,612],[568,2526,2528],{"className":2527},[889],[568,2529,2531],{"className":2530},[893],[568,2532,2534],{"className":2533},[897],[568,2535,2537],{"className":2536,"style":1350},[901],[568,2538,2539,2542],{"style":1353},[568,2540],{"className":2541,"style":910},[909],[568,2543,2545],{"className":2544},[914,915,916,917],[568,2546,2039],{"className":2547},[611,917],[568,2549,1304],{"className":2550},[1303],[568,2552,2554],{"className":2553},[897],[568,2555,2557],{"className":2556,"style":2274},[901],[568,2558],{},[568,2560],{"className":2561},[800,1756],[568,2563],{"className":2564,"style":1105},[1104],[568,2566,1159],{"className":2567},[1109],[568,2569],{"className":2570,"style":1105},[1104],[568,2572,2574,2578,2641,2644,2647,2676],{"className":2573},[602],[568,2575],{"className":2576,"style":2577},[606],"height:2.0074em;vertical-align:-0.686em;",[568,2579,2581,2584,2638],{"className":2580},[611],[568,2582],{"className":2583},[793,1756],[568,2585,2587],{"className":2586},[1698],[568,2588,2590,2630],{"className":2589},[893,1268],[568,2591,2593,2627],{"className":2592},[897],[568,2594,2597,2608,2616],{"className":2595,"style":2596},[901],"height:1.3214em;",[568,2598,2599,2602],{"style":2181},[568,2600],{"className":2601,"style":1776},[909],[568,2603,2605],{"className":2604},[611],[568,2606,2039],{"className":2607},[611],[568,2609,2610,2613],{"style":1788},[568,2611],{"className":2612,"style":1776},[909],[568,2614],{"className":2615,"style":1796},[1795],[568,2617,2618,2621],{"style":2229},[568,2619],{"className":2620,"style":1776},[909],[568,2622,2624],{"className":2623},[611],[568,2625,2048],{"className":2626},[611],[568,2628,1304],{"className":2629},[1303],[568,2631,2633],{"className":2632},[897],[568,2634,2636],{"className":2635,"style":2274},[901],[568,2637],{},[568,2639],{"className":2640},[800,1756],[568,2642],{"className":2643,"style":1251},[1104],[568,2645,819],{"className":2646,"style":856},[611,612],[568,2648,2650,2653],{"className":2649},[611],[568,2651,1702],{"className":2652,"style":1812},[611,612],[568,2654,2656],{"className":2655},[889],[568,2657,2659],{"className":2658},[893],[568,2660,2662],{"className":2661},[897],[568,2663,2665],{"className":2664,"style":2301},[901],[568,2666,2667,2670],{"style":2304},[568,2668],{"className":2669,"style":910},[909],[568,2671,2673],{"className":2672},[914,915,916,917],[568,2674,839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rechnen. Richtig ist die Differenz der Quadrate ",[568,4401,4403,4429],{"className":4402},[571],[568,4404,4406],{"className":4405},[575],[577,4407,4408],{"xmlns":579},[581,4409,4410,4426],{},[584,4411,4412,4418,4420],{},[832,4413,4414,4416],{},[587,4415,589],{},[837,4417,839],{},[760,4419,1188],{},[832,4421,4422,4424],{},[587,4423,1044],{},[837,4425,839],{},[591,4427,4428],{"encoding":593},"f^2 - g^2",[568,4430,4432,4477],{"className":4431,"ariaHidden":598},[597],[568,4433,4435,4439,4468,4471,4474],{"className":4434},[602],[568,4436],{"className":4437,"style":4438},[606],"height:1.0085em;vertical-align:-0.1944em;",[568,4440,4442,4445],{"className":4441},[611],[568,4443,589],{"className":4444,"style":613},[611,612],[568,4446,4448],{"className":4447},[889],[568,4449,4451],{"className":4450},[893],[568,4452,4454],{"className":4453},[897],[568,4455,4457],{"className":4456,"style":1350},[901],[568,4458,4459,4462],{"style":1353},[568,4460],{"className":4461,"style":910},[909],[568,4463,4465],{"className":4464},[914,915,916,917],[568,4466,839],{"className":4467},[611,917],[568,4469],{"className":4470,"style":1228},[1104],[568,4472,1188],{"className":4473},[1369],[568,4475],{"className":4476,"style":1228},[1104],[568,4478,4480,4483],{"className":4479},[602],[568,4481],{"className":4482,"style":4438},[606],[568,4484,4486,4489],{"className":4485},[611],[568,4487,1044],{"className":4488,"style":856},[611,612],[568,4490,4492],{"className":4491},[889],[568,4493,4495],{"className":4494},[893],[568,4496,4498],{"className":4497},[897],[568,4499,4501],{"className":4500,"style":1350},[901],[568,4502,4503,4506],{"style":1353},[568,4504],{"className":4505,"style":910},[909],[568,4507,4509],{"className":4508},[914,915,916,917],[568,4510,839],{"className":4511},[611,917],[4196,4513,4514,4515,4544,4545,4656,4657,4709,4710,4744,4745,4773,4774,4802,4803,1433],{},"Die Formel für eine Rotation um die ",[568,4516,4518,4532],{"className":4517},[571],[568,4519,4521],{"className":4520},[575],[577,4522,4523],{"xmlns":579},[581,4524,4525,4530],{},[584,4526,4527],{},[587,4528,4529],{},"y",[591,4531,4529],{"encoding":593},[568,4533,4535],{"className":4534,"ariaHidden":598},[597],[568,4536,4538,4541],{"className":4537},[602],[568,4539],{"className":4540,"style":1056},[606],[568,4542,4529],{"className":4543,"style":856},[611,612],"-Achse verwenden. Für ",[568,4546,4548,4573],{"className":4547},[571],[568,4549,4551],{"className":4550},[575],[577,4552,4553],{"xmlns":579},[581,4554,4555,4571],{},[584,4556,4557,4559,4561,4563,4565,4567],{},[587,4558,589],{},[760,4560,763],{"stretchy":762},[587,4562,691],{},[760,4564,768],{"stretchy":762},[760,4566,1159],{},[2708,4568,4569],{},[587,4570,691],{},[591,4572,3636],{"encoding":593},[568,4574,4576,4603],{"className":4575,"ariaHidden":598},[597],[568,4577,4579,4582,4585,4588,4591,4594,4597,4600],{"className":4578},[602],[568,4580],{"className":4581,"style":783},[606],[568,4583,589],{"className":4584,"style":613},[611,612],[568,4586,763],{"className":4587},[793],[568,4589,691],{"className":4590},[611,612],[568,4592,768],{"className":4593},[800],[568,4595],{"className":4596,"style":1105},[1104],[568,4598,1159],{"className":4599},[1109],[568,4601],{"className":4602,"style":1105},[1104],[568,4604,4606,4609],{"className":4605},[602],[568,4607],{"className":4608,"style":3673},[606],[568,4610,4612],{"className":4611},[611,2769],[568,4613,4615,4648],{"className":4614},[893,1268],[568,4616,4618,4645],{"className":4617},[897],[568,4619,4621,4633],{"className":4620,"style":3686},[901],[568,4622,4624,4627],{"className":4623,"style":2784},[2783],[568,4625],{"className":4626,"style":1776},[909],[568,4628,4630],{"className":4629,"style":2791},[611],[568,4631,691],{"className":4632},[611,612],[568,4634,4635,4638],{"style":3701},[568,4636],{"className":4637,"style":1776},[909],[568,4639,4641],{"className":4640,"style":2869},[2868],[2871,4642,4643],{"xmlns":2873,"width":2874,"height":2875,"viewBox":2876,"preserveAspectRatio":2877},[2879,4644],{"d":2881},[568,4646,1304],{"className":4647},[1303],[568,4649,4651],{"className":4650},[897],[568,4652,4654],{"className":4653,"style":3721},[901],[568,4655],{}," auf ",[568,4658,4660,4682],{"className":4659},[571],[568,4661,4663],{"className":4662},[575],[577,4664,4665],{"xmlns":579},[581,4666,4667,4679],{},[584,4668,4669,4671,4673,4675,4677],{},[760,4670,3024],{"stretchy":762},[837,4672,1075],{},[760,4674,4183],{"separator":598},[837,4676,3062],{},[760,4678,3047],{"stretchy":762},[591,4680,4681],{"encoding":593},"[0, 4]",[568,4683,4685],{"className":4684,"ariaHidden":598},[597],[568,4686,4688,4691,4694,4697,4700,4703,4706],{"className":4687},[602],[568,4689],{"className":4690,"style":783},[606],[568,4692,3024],{"className":4693},[793],[568,4695,1075],{"className":4696},[611],[568,4698,4183],{"className":4699},[4182],[568,4701],{"className":4702,"style":1251},[1104],[568,4704,3062],{"className":4705},[611],[568,4707,3047],{"className":4708},[800]," ergibt sie ",[568,4711,4713,4729],{"className":4712},[571],[568,4714,4716],{"className":4715},[575],[577,4717,4718],{"xmlns":579},[581,4719,4720,4726],{},[584,4721,4722,4724],{},[837,4723,3847],{},[587,4725,819],{},[591,4727,4728],{"encoding":593},"8\\pi",[568,4730,4732],{"className":4731,"ariaHidden":598},[597],[568,4733,4735,4738,4741],{"className":4734},[602],[568,4736],{"className":4737,"style":1660},[606],[568,4739,3847],{"className":4740},[611],[568,4742,819],{"className":4743,"style":856},[611,612]," nur bei Drehung um die ",[568,4746,4748,4761],{"className":4747},[571],[568,4749,4751],{"className":4750},[575],[577,4752,4753],{"xmlns":579},[581,4754,4755,4759],{},[584,4756,4757],{},[587,4758,691],{},[591,4760,691],{"encoding":593},[568,4762,4764],{"className":4763,"ariaHidden":598},[597],[568,4765,4767,4770],{"className":4766},[602],[568,4768],{"className":4769,"style":641},[606],[568,4771,691],{"className":4772},[611,612],"-Achse. Bei Drehung der Fläche unter dem Graphen um die ",[568,4775,4777,4790],{"className":4776},[571],[568,4778,4780],{"className":4779},[575],[577,4781,4782],{"xmlns":579},[581,4783,4784,4788],{},[584,4785,4786],{},[587,4787,4529],{},[591,4789,4529],{"encoding":593},[568,4791,4793],{"className":4792,"ariaHidden":598},[597],[568,4794,4796,4799],{"className":4795},[602],[568,4797],{"className":4798,"style":1056},[606],[568,4800,4529],{"className":4801,"style":856},[611,612],"-Achse gilt ",[568,4804,4806,4867],{"className":4805},[571],[568,4807,4809],{"className":4808},[575],[577,4810,4811],{"xmlns":579},[581,4812,4813,4864],{},[584,4814,4815,4817,4819,4821,4823,4831,4833,4835,4837,4839,4841,4843,4845,4847,4849,4857,4859,4861],{},[587,4816,1156],{},[760,4818,1159],{},[837,4820,839],{},[587,4822,819],{},[1163,4824,4825,4827,4829],{},[760,4826,1167],{},[837,4828,1075],{},[837,4830,3062],{},[587,4832,691],{},[587,4834,589],{},[760,4836,763],{"stretchy":762},[587,4838,691],{},[760,4840,768],{"stretchy":762},[1204,4842,1206],{},[587,4844,1209],{},[587,4846,691],{},[760,4848,1159],{},[1698,4850,4851,4854],{},[837,4852,4853],{},"128",[837,4855,4856],{},"5",[587,4858,819],{},[760,4860,3852],{},[837,4862,4863],{},"80,42",[591,4865,4866],{"encoding":593},"V = 2\\pi \\int_0^4 x f(x)\\,dx = \\frac{128}{5}\\pi \\approx 80{,}42",[568,4868,4870,4888,4992,5080],{"className":4869,"ariaHidden":598},[597],[568,4871,4873,4876,4879,4882,4885],{"className":4872},[602],[568,4874],{"className":4875,"style":1224},[606],[568,4877,1156],{"className":4878,"style":1228},[611,612],[568,4880],{"className":4881,"style":1105},[1104],[568,4883,1159],{"className":4884},[1109],[568,4886],{"className":4887,"style":1105},[1104],[568,4889,4891,4895,4898,4901,4904,4956,4959,4962,4965,4968,4971,4974,4977,4980,4983,4986,4989],{"className":4890},[602],[568,4892],{"className":4893,"style":4894},[606],"height:1.3648em;vertical-align:-0.3558em;",[568,4896,839],{"className":4897},[611],[568,4899,819],{"className":4900,"style":856},[611,612],[568,4902],{"className":4903,"style":1251},[1104],[568,4905,4907,4910],{"className":4906},[1255],[568,4908,1167],{"className":4909,"style":1261},[1255,1259,1260],[568,4911,4913],{"className":4912},[889],[568,4914,4916,4948],{"className":4915},[893,1268],[568,4917,4919,4945],{"className":4918},[897],[568,4920,4923,4934],{"className":4921,"style":4922},[901],"height:1.009em;",[568,4924,4925,4928],{"style":1278},[568,4926],{"className":4927,"style":910},[909],[568,4929,4931],{"className":4930},[914,915,916,917],[568,4932,1075],{"className":4933},[611,917],[568,4935,4936,4939],{"style":1290},[568,4937],{"className":4938,"style":910},[909],[568,4940,4942],{"className":4941},[914,915,916,917],[568,4943,3062],{"className":4944},[611,917],[568,4946,1304],{"className":4947},[1303],[568,4949,4951],{"className":4950},[897],[568,4952,4954],{"className":4953,"style":1311},[901],[568,4955],{},[568,4957],{"className":4958,"style":1251},[1104],[568,4960,691],{"className":4961},[611,612],[568,4963,589],{"className":4964,"style":613},[611,612],[568,4966,763],{"className":4967},[793],[568,4969,691],{"className":4970},[611,612],[568,4972,768],{"className":4973},[800],[568,4975],{"className":4976,"style":1251},[1104],[568,4978,1209],{"className":4979},[611,612],[568,4981,691],{"className":4982},[611,612],[568,4984],{"className":4985,"style":1105},[1104],[568,4987,1159],{"className":4988},[1109],[568,4990],{"className":4991,"style":1105},[1104],[568,4993,4995,4999,5068,5071,5074,5077],{"className":4994},[602],[568,4996],{"className":4997,"style":4998},[606],"height:1.1901em;vertical-align:-0.345em;",[568,5000,5002,5005,5065],{"className":5001},[611],[568,5003],{"className":5004},[793,1756],[568,5006,5008],{"className":5007},[1698],[568,5009,5011,5057],{"className":5010},[893,1268],[568,5012,5014,5054],{"className":5013},[897],[568,5015,5018,5032,5040],{"className":5016,"style":5017},[901],"height:0.8451em;",[568,5019,5020,5023],{"style":1772},[568,5021],{"className":5022,"style":1776},[909],[568,5024,5026],{"className":5025},[914,915,916,917],[568,5027,5029],{"className":5028},[611,917],[568,5030,4856],{"className":5031},[611,917],[568,5033,5034,5037],{"style":1788},[568,5035],{"className":5036,"style":1776},[909],[568,5038],{"className":5039,"style":1796},[1795],[568,5041,5042,5045],{"style":1799},[568,5043],{"className":5044,"style":1776},[909],[568,5046,5048],{"className":5047},[914,915,916,917],[568,5049,5051],{"className":5050},[611,917],[568,5052,4853],{"className":5053},[611,917],[568,5055,1304],{"className":5056},[1303],[568,5058,5060],{"className":5059},[897],[568,5061,5063],{"className":5062,"style":1822},[901],[568,5064],{},[568,5066],{"className":5067},[800,1756],[568,5069,819],{"className":5070,"style":856},[611,612],[568,5072],{"className":5073,"style":1105},[1104],[568,5075,3852],{"className":5076},[1109],[568,5078],{"className":5079,"style":1105},[1104],[568,5081,5083,5086,5090,5096],{"className":5082},[602],[568,5084],{"className":5085,"style":4171},[606],[568,5087,5089],{"className":5088},[611],"80",[568,5091,5093],{"className":5092},[611],[568,5094,4183],{"className":5095},[4182],[568,5097,5099],{"className":5098},[611],"42",{"title":5101,"searchDepth":5102,"depth":5102,"links":5103},"",2,[5104,5105,5106,5107],{"id":561,"depth":5102,"text":562},{"id":1436,"depth":5102,"text":1437},{"id":1667,"depth":5102,"text":1668},{"id":4190,"depth":5102,"text":4191},[5109,5112,5115,5118,5121,5124,5127,5129],{"lhs":5110,"rhs":5111},"pi * (r\u002Fh)^2 * (h^3\u002F3 - 0)","1\u002F3 * pi * r^2 * h",{"lhs":5113,"rhs":5114},"pi * ((r^2*r - r^3\u002F3) - (r^2*(-r) - (-r)^3\u002F3))","4\u002F3 * pi * r^3",{"lhs":5116,"rhs":5117},"pi * (4^2\u002F2 - 0)","8 * pi",{"lhs":5119,"rhs":5120},"round(8 * pi, 2)","25.13",{"lhs":5122,"rhs":5123},"2 * pi * (2\u002F5 * 4^(5\u002F2))","128\u002F5 * pi",{"lhs":5125,"rhs":5126},"round(128\u002F5 * pi, 2)","80.42",{"lhs":5128,"rhs":5126},"round(2 * pi * sum(map(0:999, f(k) = ((k + 0.5) * 4 \u002F 1000)^(3\u002F2))) * 4 \u002F 1000, 2)",{"lhs":5130,"rhs":5131},"round(pi * sum(map(0:999, f(k) = sqrt((k + 0.5) * 4 \u002F 1000)^2)) * 4 \u002F 1000, 4)","round(8 * pi, 4)","f \\text{ stetig auf } [a, b],\\ a \u003C b,\\ \\text{Rotation um die } x\\text{-Achse}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">stetig auf\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">[a, b],\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"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=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo 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class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.511em;vertical-align:-0.9119em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.599em;\">\u003Cspan 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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>",{"symbol":589,"meaning":5201,"symbolHtml":5202},"Funktion, deren Graph um die x-Achse rotiert","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5204,"meaning":5205,"symbolHtml":5206},"a, b","Grenzen des rotierenden Abschnitts","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan 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