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Mittelwert wird also tatsächlich als Funktionswert angenommen. Das folgt aus dem Zwischenwertsatz, weil ",[571,1166,1168,1186],{"className":1167},[574],[571,1169,1171],{"className":1170},[578],[580,1172,1173],{"xmlns":582},[584,1174,1175,1183],{},[587,1176,1177],{},[809,1178,1179,1181],{"accent":609},[590,1180,661],{},[594,1182,815],{},[601,1184,1185],{"encoding":603},"\\bar f",[571,1187,1189],{"className":1188,"ariaHidden":609},[608],[571,1190,1192,1195],{"className":1191},[613],[571,1193],{"className":1194,"style":884},[617],[571,1196,1198],{"className":1197},[622,888],[571,1199,1201,1229],{"className":1200},[892,893],[571,1202,1204,1226],{"className":1203},[897],[571,1205,1207,1215],{"className":1206,"style":902},[901],[571,1208,1209,1212],{"style":905},[571,1210],{"className":1211,"style":910},[909],[571,1213,661],{"className":1214,"style":688},[622,623],[571,1216,1217,1220],{"style":916},[571,1218],{"className":1219,"style":910},[909],[571,1221,1223],{"className":1222,"style":924},[923],[571,1224,815],{"className":1225},[622],[571,1227,932],{"className":1228},[931],[571,1230,1232],{"className":1231},[897],[571,1233,1235],{"className":1234,"style":939},[901],[571,1236],{}," zwischen Minimum und Maximum von ",[571,1239,1241,1254],{"className":1240},[574],[571,1242,1244],{"className":1243},[578],[580,1245,1246],{"xmlns":582},[584,1247,1248,1252],{},[587,1249,1250],{},[590,1251,661],{},[601,1253,661],{"encoding":603},[571,1255,1257],{"className":1256,"ariaHidden":609},[608],[571,1258,1260,1263],{"className":1259},[613],[571,1261],{"className":1262,"style":728},[617],[571,1264,661],{"className":1265,"style":688},[622,623]," auf ",[571,1268,1270,1295],{"className":1269},[574],[571,1271,1273],{"className":1272},[578],[580,1274,1275],{"xmlns":582},[584,1276,1277,1292],{},[587,1278,1279,1282,1284,1287,1289],{},[594,1280,1281],{"stretchy":664},"[",[590,1283,599],{},[594,1285,1286],{"separator":609},",",[590,1288,592],{},[594,1290,1291],{"stretchy":664},"]",[601,1293,1294],{"encoding":603},"[a, b]",[571,1296,1298],{"className":1297,"ariaHidden":609},[608],[571,1299,1301,1304,1307,1310,1314,1317,1320],{"className":1300},[613],[571,1302],{"className":1303,"style":684},[617],[571,1305,1281],{"className":1306},[692],[571,1308,599],{"className":1309},[622,623],[571,1311,1286],{"className":1312},[1313],"mpunct",[571,1315],{"className":1316,"style":1045},[627],[571,1318,592],{"className":1319},[622,623],[571,1321,1291],{"className":1322},[700]," liegt.",[563,1325,1326,1329,1330,1266,1361,1412,1413,1468,1469,1544],{},[567,1327,1328],{},"Verallgemeinerung mit Gewicht:"," Ist zusätzlich ",[571,1331,1333,1347],{"className":1332},[574],[571,1334,1336],{"className":1335},[578],[580,1337,1338],{"xmlns":582},[584,1339,1340,1345],{},[587,1341,1342],{},[590,1343,1344],{},"g",[601,1346,1344],{"encoding":603},[571,1348,1350],{"className":1349,"ariaHidden":609},[608],[571,1351,1353,1357],{"className":1352},[613],[571,1354],{"className":1355,"style":1356},[617],"height:0.625em;vertical-align:-0.1944em;",[571,1358,1344],{"className":1359,"style":1360},[622,623],"margin-right:0.0359em;",[571,1362,1364,1385],{"className":1363},[574],[571,1365,1367],{"className":1366},[578],[580,1368,1369],{"xmlns":582},[584,1370,1371,1383],{},[587,1372,1373,1375,1377,1379,1381],{},[594,1374,1281],{"stretchy":664},[590,1376,599],{},[594,1378,1286],{"separator":609},[590,1380,592],{},[594,1382,1291],{"stretchy":664},[601,1384,1294],{"encoding":603},[571,1386,1388],{"className":1387,"ariaHidden":609},[608],[571,1389,1391,1394,1397,1400,1403,1406,1409],{"className":1390},[613],[571,1392],{"className":1393,"style":684},[617],[571,1395,1281],{"className":1396},[692],[571,1398,599],{"className":1399},[622,623],[571,1401,1286],{"className":1402},[1313],[571,1404],{"className":1405,"style":1045},[627],[571,1407,592],{"className":1408},[622,623],[571,1410,1291],{"className":1411},[700]," stetig und wechselt nicht das Vorzeichen (z.B. ",[571,1414,1416,1436],{"className":1415},[574],[571,1417,1419],{"className":1418},[578],[580,1420,1421],{"xmlns":582},[584,1422,1423,1433],{},[587,1424,1425,1427,1430],{},[590,1426,1344],{},[594,1428,1429],{},"≥",[823,1431,1432],{},"0",[601,1434,1435],{"encoding":603},"g \\geq 0",[571,1437,1439,1458],{"className":1438,"ariaHidden":609},[608],[571,1440,1442,1446,1449,1452,1455],{"className":1441},[613],[571,1443],{"className":1444,"style":1445},[617],"height:0.8304em;vertical-align:-0.1944em;",[571,1447,1344],{"className":1448,"style":1360},[622,623],[571,1450],{"className":1451,"style":945},[627],[571,1453,1429],{"className":1454},[949],[571,1456],{"className":1457,"style":945},[627],[571,1459,1461,1465],{"className":1460},[613],[571,1462],{"className":1463,"style":1464},[617],"height:0.6444em;",[571,1466,1432],{"className":1467},[622],"), dann gibt es ein ",[571,1470,1472,1499],{"className":1471},[574],[571,1473,1475],{"className":1474},[578],[580,1476,1477],{"xmlns":582},[584,1478,1479,1496],{},[587,1480,1481,1483,1486,1488,1490,1492,1494],{},[590,1482,668],{},[594,1484,1485],{},"∈",[594,1487,1281],{"stretchy":664},[590,1489,599],{},[594,1491,1286],{"separator":609},[590,1493,592],{},[594,1495,1291],{"stretchy":664},[601,1497,1498],{"encoding":603},"\\xi \\in [a, b]",[571,1500,1502,1520],{"className":1501,"ariaHidden":609},[608],[571,1503,1505,1508,1511,1514,1517],{"className":1504},[613],[571,1506],{"className":1507,"style":728},[617],[571,1509,668],{"className":1510,"style":696},[622,623],[571,1512],{"className":1513,"style":945},[627],[571,1515,1485],{"className":1516},[949],[571,1518],{"className":1519,"style":945},[627],[571,1521,1523,1526,1529,1532,1535,1538,1541],{"className":1522},[613],[571,1524],{"className":1525,"style":684},[617],[571,1527,1281],{"className":1528},[692],[571,1530,599],{"className":1531},[622,623],[571,1533,1286],{"className":1534},[1313],[571,1536],{"className":1537,"style":1045},[627],[571,1539,592],{"className":1540},[622,623],[571,1542,1291],{"className":1543},[700]," mit",[571,1546,1548],{"className":1547},[794],[571,1549,1551,1627],{"className":1550},[574],[571,1552,1554],{"className":1553},[578],[580,1555,1556],{"xmlns":582,"display":803},[584,1557,1558,1624],{},[587,1559,1560,1568,1570,1572,1574,1576,1578,1580,1582,1584,1586,1588,1590,1592,1594,1596,1598,1600,1602,1610,1612,1614,1616,1618,1620,1622],{},[835,1561,1562,1564,1566],{},[594,1563,839],{},[590,1565,599],{},[590,1567,592],{},[590,1569,661],{},[594,1571,665],{"stretchy":664},[590,1573,850],{},[594,1575,671],{"stretchy":664},[854,1577,856],{},[590,1579,1344],{},[594,1581,665],{"stretchy":664},[590,1583,850],{},[594,1585,671],{"stretchy":664},[854,1587,856],{},[590,1589,859],{},[590,1591,850],{},[594,1593,818],{},[590,1595,661],{},[594,1597,665],{"stretchy":664},[590,1599,668],{},[594,1601,671],{"stretchy":664},[835,1603,1604,1606,1608],{},[594,1605,839],{},[590,1607,599],{},[590,1609,592],{},[590,1611,1344],{},[594,1613,665],{"stretchy":664},[590,1615,850],{},[594,1617,671],{"stretchy":664},[854,1619,856],{},[590,1621,859],{},[590,1623,850],{},[601,1625,1626],{"encoding":603},"\\int_a^b f(x)\\,g(x)\\,dx = f(\\xi) \\int_a^b g(x)\\,dx",[571,1628,1630,1735],{"className":1629,"ariaHidden":609},[608],[571,1631,1633,1636,1687,1690,1693,1696,1699,1702,1705,1708,1711,1714,1717,1720,1723,1726,1729,1732],{"className":1632},[613],[571,1634],{"className":1635,"style":959},[617],[571,1637,1639,1642],{"className":1638},[1049],[571,1640,839],{"className":1641,"style":1055},[1049,1053,1054],[571,1643,1645],{"className":1644},[1059],[571,1646,1648,1679],{"className":1647},[892,893],[571,1649,1651,1676],{"className":1650},[897],[571,1652,1654,1665],{"className":1653,"style":1069},[901],[571,1655,1656,1659],{"style":1072},[571,1657],{"className":1658,"style":1076},[909],[571,1660,1662],{"className":1661},[1080,1081,1082,1083],[571,1663,599],{"className":1664},[622,623,1083],[571,1666,1667,1670],{"style":1089},[571,1668],{"className":1669,"style":1076},[909],[571,1671,1673],{"className":1672},[1080,1081,1082,1083],[571,1674,592],{"className":1675},[622,623,1083],[571,1677,932],{"className":1678},[931],[571,1680,1682],{"className":1681},[897],[571,1683,1685],{"className":1684,"style":1108},[901],[571,1686],{},[571,1688],{"className":1689,"style":1045},[627],[571,1691,661],{"className":1692,"style":688},[622,623],[571,1694,665],{"className":1695},[692],[571,1697,850],{"className":1698},[622,623],[571,1700,671],{"className":1701},[700],[571,1703],{"className":1704,"style":1045},[627],[571,1706,1344],{"className":1707,"style":1360},[622,623],[571,1709,665],{"className":1710},[692],[571,1712,850],{"className":1713},[622,623],[571,1715,671],{"className":1716},[700],[571,1718],{"className":1719,"style":1045},[627],[571,1721,859],{"className":1722},[622,623],[571,1724,850],{"className":1725},[622,623],[571,1727],{"className":1728,"style":945},[627],[571,1730,818],{"className":1731},[949],[571,1733],{"className":1734,"style":945},[627],[571,1736,1738,1741,1744,1747,1750,1753,1756,1807,1810,1813,1816,1819,1822,1825,1828],{"className":1737},[613],[571,1739],{"className":1740,"style":959},[617],[571,1742,661],{"className":1743,"style":688},[622,623],[571,1745,665],{"className":1746},[692],[571,1748,668],{"className":1749,"style":696},[622,623],[571,1751,671],{"className":1752},[700],[571,1754],{"className":1755,"style":1045},[627],[571,1757,1759,1762],{"className":1758},[1049],[571,1760,839],{"className":1761,"style":1055},[1049,1053,1054],[571,1763,1765],{"className":1764},[1059],[571,1766,1768,1799],{"className":1767},[892,893],[571,1769,1771,1796],{"className":1770},[897],[571,1772,1774,1785],{"className":1773,"style":1069},[901],[571,1775,1776,1779],{"style":1072},[571,1777],{"className":1778,"style":1076},[909],[571,1780,1782],{"className":1781},[1080,1081,1082,1083],[571,1783,599],{"className":1784},[622,623,1083],[571,1786,1787,1790],{"style":1089},[571,1788],{"className":1789,"style":1076},[909],[571,1791,1793],{"className":1792},[1080,1081,1082,1083],[571,1794,592],{"className":1795},[622,623,1083],[571,1797,932],{"className":1798},[931],[571,1800,1802],{"className":1801},[897],[571,1803,1805],{"className":1804,"style":1108},[901],[571,1806],{},[571,1808],{"className":1809,"style":1045},[627],[571,1811,1344],{"className":1812,"style":1360},[622,623],[571,1814,665],{"className":1815},[692],[571,1817,850],{"className":1818},[622,623],[571,1820,671],{"className":1821},[700],[571,1823],{"className":1824,"style":1045},[627],[571,1826,859],{"className":1827},[622,623],[571,1829,850],{"className":1830},[622,623],[563,1832,1833,1834,1266,1937,1989,1990,2094,2095,2300,2301,732],{},"Mit ",[571,1835,1837,1871],{"className":1836},[574],[571,1838,1840],{"className":1839},[578],[580,1841,1842],{"xmlns":582},[584,1843,1844,1868],{},[587,1845,1846,1848,1850,1852,1854,1856,1858,1860,1862,1864,1866],{},[590,1847,661],{},[594,1849,665],{"stretchy":664},[590,1851,850],{},[594,1853,671],{"stretchy":664},[594,1855,818],{},[590,1857,1344],{},[594,1859,665],{"stretchy":664},[590,1861,850],{},[594,1863,671],{"stretchy":664},[594,1865,818],{},[590,1867,850],{},[601,1869,1870],{"encoding":603},"f(x) = g(x) = x",[571,1872,1874,1901,1928],{"className":1873,"ariaHidden":609},[608],[571,1875,1877,1880,1883,1886,1889,1892,1895,1898],{"className":1876},[613],[571,1878],{"className":1879,"style":684},[617],[571,1881,661],{"className":1882,"style":688},[622,623],[571,1884,665],{"className":1885},[692],[571,1887,850],{"className":1888},[622,623],[571,1890,671],{"className":1891},[700],[571,1893],{"className":1894,"style":945},[627],[571,1896,818],{"className":1897},[949],[571,1899],{"className":1900,"style":945},[627],[571,1902,1904,1907,1910,1913,1916,1919,1922,1925],{"className":1903},[613],[571,1905],{"className":1906,"style":684},[617],[571,1908,1344],{"className":1909,"style":1360},[622,623],[571,1911,665],{"className":1912},[692],[571,1914,850],{"className":1915},[622,623],[571,1917,671],{"className":1918},[700],[571,1920],{"className":1921,"style":945},[627],[571,1923,818],{"className":1924},[949],[571,1926],{"className":1927,"style":945},[627],[571,1929,1931,1934],{"className":1930},[613],[571,1932],{"className":1933,"style":642},[617],[571,1935,850],{"className":1936},[622,623],[571,1938,1940,1962],{"className":1939},[574],[571,1941,1943],{"className":1942},[578],[580,1944,1945],{"xmlns":582},[584,1946,1947,1959],{},[587,1948,1949,1951,1953,1955,1957],{},[594,1950,1281],{"stretchy":664},[823,1952,1432],{},[594,1954,1286],{"separator":609},[823,1956,825],{},[594,1958,1291],{"stretchy":664},[601,1960,1961],{"encoding":603},"[0, 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und ",[571,2096,2098,2135],{"className":2097},[574],[571,2099,2101],{"className":2100},[578],[580,2102,2103],{"xmlns":582},[584,2104,2105,2132],{},[587,2106,2107,2115,2117,2119,2121,2123,2125],{},[835,2108,2109,2111,2113],{},[594,2110,839],{},[823,2112,1432],{},[823,2114,825],{},[590,2116,850],{},[854,2118,856],{},[590,2120,859],{},[590,2122,850],{},[594,2124,818],{},[820,2126,2127,2129],{},[823,2128,825],{},[823,2130,2131],{},"2",[601,2133,2134],{"encoding":603},"\\int_0^1 x\\,dx = \\frac{1}{2}",[571,2136,2138,2226],{"className":2137,"ariaHidden":609},[608],[571,2139,2141,2145,2202,2205,2208,2211,2214,2217,2220,2223],{"className":2140},[613],[571,2142],{"className":2143,"style":2144},[617],"height:1.3648em;vertical-align:-0.3558em;",[571,2146,2148,2153],{"className":2147},[1049],[571,2149,839],{"className":2150,"style":2152},[1049,1053,2151],"small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[571,2154,2156],{"className":2155},[1059],[571,2157,2159,2193],{"className":2158},[892,893],[571,2160,2162,2190],{"className":2161},[897],[571,2163,2166,2178],{"className":2164,"style":2165},[901],"height:1.009em;",[571,2167,2169,2172],{"style":2168},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[571,2170],{"className":2171,"style":1076},[909],[571,2173,2175],{"className":2174},[1080,1081,1082,1083],[571,2176,1432],{"className":2177},[622,1083],[571,2179,2181,2184],{"style":2180},"top:-3.2579em;margin-right:0.05em;",[571,2182],{"className":2183,"style":1076},[909],[571,2185,2187],{"className":2186},[1080,1081,1082,1083],[571,2188,825],{"className":2189},[622,1083],[571,2191,932],{"className":2192},[931],[571,2194,2196],{"className":2195},[897],[571,2197,2200],{"className":2198,"style":2199},[901],"height:0.3558em;",[571,2201],{},[571,2203],{"className":2204,"style":1045},[627],[571,2206,850],{"className":2207},[622,623],[571,2209],{"className":2210,"style":1045},[627],[571,2212,859],{"className":2213},[622,623],[571,2215,850],{"className":2216},[622,623],[571,2218],{"className":2219,"style":945},[627],[571,2221,818],{"className":2222},[949],[571,2224],{"className":2225,"style":945},[627],[571,2227,2229,2232],{"className":2228},[613],[571,2230],{"className":2231,"style":2021},[617],[571,2233,2235,2238,2297],{"className":2234},[622],[571,2236],{"className":2237},[692,966],[571,2239,2241],{"className":2240},[820],[571,2242,2244,2289],{"className":2243},[892,893],[571,2245,2247,2286],{"className":2246},[897],[571,2248,2250,2264,2272],{"className":2249,"style":2040},[901],[571,2251,2252,2255],{"style":2043},[571,2253],{"className":2254,"style":910},[909],[571,2256,2258],{"className":2257},[1080,1081,1082,1083],[571,2259,2261],{"className":2260},[622,1083],[571,2262,2131],{"className":2263},[622,1083],[571,2265,2266,2269],{"style":1006},[571,2267],{"className":2268,"style":910},[909],[571,2270],{"className":2271,"style":1014},[1013],[571,2273,2274,2277],{"style":2066},[571,2275],{"className":2276,"style":910},[909],[571,2278,2280],{"className":2279},[1080,1081,1082,1083],[571,2281,2283],{"className":2282},[622,1083],[571,2284,825],{"className":2285},[622,1083],[571,2287,932],{"className":2288},[931],[571,2290,2292],{"className":2291},[897],[571,2293,2295],{"className":2294,"style":2088},[901],[571,2296],{},[571,2298],{"className":2299},[700,966],", also ",[571,2302,2304,2326],{"className":2303},[574],[571,2305,2307],{"className":2306},[578],[580,2308,2309],{"xmlns":582},[584,2310,2311,2323],{},[587,2312,2313,2315,2317],{},[590,2314,668],{},[594,2316,818],{},[820,2318,2319,2321],{},[823,2320,2131],{},[823,2322,2008],{},[601,2324,2325],{"encoding":603},"\\xi = \\frac{2}{3}",[571,2327,2329,2347],{"className":2328,"ariaHidden":609},[608],[571,2330,2332,2335,2338,2341,2344],{"className":2331},[613],[571,2333],{"className":2334,"style":728},[617],[571,2336,668],{"className":2337,"style":696},[622,623],[571,2339],{"className":2340,"style":945},[627],[571,2342,818],{"className":2343},[949],[571,2345],{"className":2346,"style":945},[627],[571,2348,2350,2353],{"className":2349},[613],[571,2351],{"className":2352,"style":2021},[617],[571,2354,2356,2359,2418],{"className":2355},[622],[571,2357],{"className":2358},[692,966],[571,2360,2362],{"className":2361},[820],[571,2363,2365,2410],{"className":2364},[892,893],[571,2366,2368,2407],{"className":2367},[897],[571,2369,2371,2385,2393],{"className":2370,"style":2040},[901],[571,2372,2373,2376],{"style":2043},[571,2374],{"className":2375,"style":910},[909],[571,2377,2379],{"className":2378},[1080,1081,1082,1083],[571,2380,2382],{"className":2381},[622,1083],[571,2383,2008],{"className":2384},[622,1083],[571,2386,2387,2390],{"style":1006},[571,2388],{"className":2389,"style":910},[909],[571,2391],{"className":2392,"style":1014},[1013],[571,2394,2395,2398],{"style":2066},[571,2396],{"className":2397,"style":910},[909],[571,2399,2401],{"className":2400},[1080,1081,1082,1083],[571,2402,2404],{"className":2403},[622,1083],[571,2405,2131],{"className":2406},[622,1083],[571,2408,932],{"className":2409},[931],[571,2411,2413],{"className":2412},[897],[571,2414,2416],{"className":2415,"style":2088},[901],[571,2417],{},[571,2419],{"className":2420},[700,966],[563,2422,2423,2424,2427,2428,2617,2618,2647],{},"Der Satz wird vor allem für ",[567,2425,2426],{},"Abschätzungen"," benutzt, z.B. um zu zeigen, dass ",[571,2429,2431,2489],{"className":2430},[574],[571,2432,2434],{"className":2433},[578],[580,2435,2436],{"xmlns":582},[584,2437,2438,2486],{},[587,2439,2440,2456,2458,2460,2463,2465,2467,2469,2471,2474,2476,2478,2480,2482,2484],{},[835,2441,2442,2444,2446],{},[594,2443,839],{},[590,2445,850],{},[587,2447,2448,2450,2453],{},[590,2449,850],{},[594,2451,2452],{},"+",[590,2454,2455],{},"h",[590,2457,661],{},[594,2459,665],{"stretchy":664},[590,2461,2462],{},"t",[594,2464,671],{"stretchy":664},[854,2466,856],{},[590,2468,859],{},[590,2470,2462],{},[594,2472,2473],{},"≈",[590,2475,661],{},[594,2477,665],{"stretchy":664},[590,2479,850],{},[594,2481,671],{"stretchy":664},[854,2483,856],{},[590,2485,2455],{},[601,2487,2488],{"encoding":603},"\\int_x^{x+h} f(t)\\,dt \\approx 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für kleine ",[571,2619,2621,2634],{"className":2620},[574],[571,2622,2624],{"className":2623},[578],[580,2625,2626],{"xmlns":582},[584,2627,2628,2632],{},[587,2629,2630],{},[590,2631,2455],{},[601,2633,2455],{"encoding":603},[571,2635,2637],{"className":2636,"ariaHidden":609},[608],[571,2638,2640,2644],{"className":2639},[613],[571,2641],{"className":2642,"style":2643},[617],"height:0.6944em;",[571,2645,2455],{"className":2646},[622,623]," ist. Daraus folgt der Hauptsatz der Differential- und Integralrechnung.",[558,2649,2651],{"id":2650},"beispiele","Beispiele",[563,2653,2654,1266,2753,2805,2806,2928,2929,3049,3050,3132,3133,732],{},[571,2655,2657,2686],{"className":2656},[574],[571,2658,2660],{"className":2659},[578],[580,2661,2662],{"xmlns":582},[584,2663,2664,2683],{},[587,2665,2666,2668,2670,2672,2674,2676],{},[590,2667,661],{},[594,2669,665],{"stretchy":664},[590,2671,850],{},[594,2673,671],{"stretchy":664},[594,2675,818],{},[2677,2678,2679,2681],"msup",{},[590,2680,850],{},[823,2682,2131],{},[601,2684,2685],{"encoding":603},"f(x) = 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3]",[571,2779,2781],{"className":2780,"ariaHidden":609},[608],[571,2782,2784,2787,2790,2793,2796,2799,2802],{"className":2783},[613],[571,2785],{"className":2786,"style":684},[617],[571,2788,1281],{"className":2789},[692],[571,2791,1432],{"className":2792},[622],[571,2794,1286],{"className":2795},[1313],[571,2797],{"className":2798,"style":1045},[627],[571,2800,2008],{"className":2801},[622],[571,2803,1291],{"className":2804},[700],": Das Integral ist ",[571,2807,2809,2833],{"className":2808},[574],[571,2810,2812],{"className":2811},[578],[580,2813,2814],{"xmlns":582},[584,2815,2816,2830],{},[587,2817,2818,2825,2827],{},[820,2819,2820,2823],{},[823,2821,2822],{},"27",[823,2824,2008],{},[594,2826,818],{},[823,2828,2829],{},"9",[601,2831,2832],{"encoding":603},"\\frac{27}{3} = 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Er wird an zwei Stellen angenommen:",[571,3577,3579],{"className":3578},[794],[571,3580,3582,3647],{"className":3581},[574],[571,3583,3585],{"className":3584},[578],[580,3586,3587],{"xmlns":582,"display":803},[584,3588,3589,3644],{},[587,3590,3591,3598,3600,3603,3605,3611,3613,3616,3618,3621,3627,3629,3631,3633,3639,3641],{},[3592,3593,3594,3596],"msub",{},[590,3595,668],{},[823,3597,825],{},[594,3599,818],{},[590,3601,3602],{},"arcsin",[594,3604,3311],{},[820,3606,3607,3609],{},[823,3608,2131],{},[590,3610,3383],{},[594,3612,2473],{},[823,3614,3615],{},"0,6901",[594,3617,1286],{"separator":609},[627,3619],{"width":3620},"2em",[3592,3622,3623,3625],{},[590,3624,668],{},[823,3626,2131],{},[594,3628,818],{},[590,3630,3383],{},[594,3632,596],{},[3592,3634,3635,3637],{},[590,3636,668],{},[823,3638,825],{},[594,3640,2473],{},[823,3642,3643],{},"2,4515",[601,3645,3646],{"encoding":603},"\\xi_1 = \\arcsin\\frac{2}{\\pi} \\approx 0{,}6901,\\qquad \\xi_2 = \\pi - \\xi_1 \\approx 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71,3952,2131],{"className":3953},[622],[571,3955,3957],{"className":3956},[622],[571,3958,1286],{"className":3959},[1313],[571,3961,3963],{"className":3962},[622],"4515",[558,3965,3967],{"id":3966},"typische-fehler","Typische Fehler",[3969,3970,3971,4281,4826],"ul",{},[3972,3973,3974,3975,1266,4026,2094,4078,1266,4129,4181,4182,4280],"li",{},"Die Stetigkeit übergehen. Die Sprungfunktion mit ",[571,3976,3978,3996],{"className":3977},[574],[571,3979,3981],{"className":3980},[578],[580,3982,3983],{"xmlns":582},[584,3984,3985,3993],{},[587,3986,3987,3989,3991],{},[590,3988,661],{},[594,3990,818],{},[823,3992,1432],{},[601,3994,3995],{"encoding":603},"f = 0",[571,3997,3999,4017],{"className":3998,"ariaHidden":609},[608],[571,4000,4002,4005,4008,4011,4014],{"className":4001},[613],[571,4003],{"className":4004,"style":728},[617],[571,4006,661],{"className":4007,"style":688},[622,623],[571,4009],{"className":4010,"style":945},[627],[571,4012,818],{"className":4013},[949],[571,4015],{"className":4016,"style":945},[627],[571,4018,4020,4023],{"className":4019},[613],[571,4021],{"className":4022,"style":1464},[617],[571,4024,1432],{"className":4025},[622],[571,4027,4029,4051],{"className":4028},[574],[571,4030,4032],{"className":4031},[578],[580,4033,4034],{"xmlns":582},[584,4035,4036,4048],{},[587,4037,4038,4040,4042,4044,4046],{},[594,4039,1281],{"stretchy":664},[823,4041,1432],{},[594,4043,1286],{"separator":609},[823,4045,825],{},[594,4047,671],{"stretchy":664},[601,4049,4050],{"encoding":603},"[0, 1)",[571,4052,4054],{"className":4053,"ariaHidden":609},[608],[571,4055,4057,4060,4063,4066,4069,4072,4075],{"className":4056},[613],[571,4058],{"className":4059,"style":684},[617],[571,4061,1281],{"className":4062},[692],[571,4064,1432],{"className":4065},[622],[571,4067,1286],{"className":4068},[1313],[571,4070],{"className":4071,"style":1045},[627],[571,4073,825],{"className":4074},[622],[571,4076,671],{"className":4077},[700],[571,4079,4081,4099],{"className":4080},[574],[571,4082,4084],{"className":4083},[578],[580,4085,4086],{"xmlns":582},[584,4087,4088,4096],{},[587,4089,4090,4092,4094],{},[590,4091,661],{},[594,4093,818],{},[823,4095,825],{},[601,4097,4098],{"encoding":603},"f = 1",[571,4100,4102,4120],{"className":4101,"ariaHidden":609},[608],[571,4103,4105,4108,4111,4114,4117],{"className":4104},[613],[571,4106],{"className":4107,"style":728},[617],[571,4109,661],{"className":4110,"style":688},[622,623],[571,4112],{"className":4113,"style":945},[627],[571,4115,818],{"className":4116},[949],[571,4118],{"className":4119,"style":945},[627],[571,4121,4123,4126],{"className":4122},[613],[571,4124],{"className":4125,"style":1464},[617],[571,4127,825],{"className":4128},[622],[571,4130,4132,4154],{"className":4131},[574],[571,4133,4135],{"className":4134},[578],[580,4136,4137],{"xmlns":582},[584,4138,4139,4151],{},[587,4140,4141,4143,4145,4147,4149],{},[594,4142,1281],{"stretchy":664},[823,4144,825],{},[594,4146,1286],{"separator":609},[823,4148,2131],{},[594,4150,1291],{"stretchy":664},[601,4152,4153],{"encoding":603},"[1, 2]",[571,4155,4157],{"className":4156,"ariaHidden":609},[608],[571,4158,4160,4163,4166,4169,4172,4175,4178],{"className":4159},[613],[571,4161],{"className":4162,"style":684},[617],[571,4164,1281],{"className":4165},[692],[571,4167,825],{"className":4168},[622],[571,4170,1286],{"className":4171},[1313],[571,4173],{"className":4174,"style":1045},[627],[571,4176,2131],{"className":4177},[622],[571,4179,1291],{"className":4180},[700]," hat den Mittelwert ",[571,4183,4185,4203],{"className":4184},[574],[571,4186,4188],{"className":4187},[578],[580,4189,4190],{"xmlns":582},[584,4191,4192,4200],{},[587,4193,4194],{},[820,4195,4196,4198],{},[823,4197,825],{},[823,4199,2131],{},[601,4201,4202],{"encoding":603},"\\frac{1}{2}",[571,4204,4206],{"className":4205,"ariaHidden":609},[608],[571,4207,4209,4212],{"className":4208},[613],[571,4210],{"className":4211,"style":2021},[617],[571,4213,4215,4218,4277],{"className":4214},[622],[571,4216],{"className":4217},[692,966],[571,4219,4221],{"className":4220},[820],[571,4222,4224,4269],{"className":4223},[892,893],[571,4225,4227,4266],{"className":4226},[897],[571,4228,4230,4244,4252],{"className":4229,"style":2040},[901],[571,4231,4232,4235],{"style":2043},[571,4233],{"className":4234,"style":910},[909],[571,4236,4238],{"className":4237},[1080,1081,1082,1083],[571,4239,4241],{"className":4240},[622,1083],[571,4242,2131],{"className":4243},[622,1083],[571,4245,4246,4249],{"style":1006},[571,4247],{"className":4248,"style":910},[909],[571,4250],{"className":4251,"style":1014},[1013],[571,4253,4254,4257],{"style":2066},[571,4255],{"className":4256,"style":910},[909],[571,4258,4260],{"className":4259},[1080,1081,1082,1083],[571,4261,4263],{"className":4262},[622,1083],[571,4264,825],{"className":4265},[622,1083],[571,4267,932],{"className":4268},[931],[571,4270,4272],{"className":4271},[897],[571,4273,4275],{"className":4274,"style":2088},[901],[571,4276],{},[571,4278],{"className":4279},[700,966],", nimmt diesen Wert aber nirgends an.",[3972,4282,4283,4284,1266,4350,4407,4408,4483,4484,4550,4551,4768,4769,4797,4798,732],{},"In der Verallgemeinerung ein Gewicht mit Vorzeichenwechsel benutzen. Für ",[571,4285,4287,4311],{"className":4286},[574],[571,4288,4290],{"className":4289},[578],[580,4291,4292],{"xmlns":582},[584,4293,4294,4308],{},[587,4295,4296,4298,4300,4302,4304,4306],{},[590,4297,1344],{},[594,4299,665],{"stretchy":664},[590,4301,850],{},[594,4303,671],{"stretchy":664},[594,4305,818],{},[590,4307,850],{},[601,4309,4310],{"encoding":603},"g(x) = x",[571,4312,4314,4341],{"className":4313,"ariaHidden":609},[608],[571,4315,4317,4320,4323,4326,4329,4332,4335,4338],{"className":4316},[613],[571,4318],{"className":4319,"style":684},[617],[571,4321,1344],{"className":4322,"style":1360},[622,623],[571,4324,665],{"className":4325},[692],[571,4327,850],{"className":4328},[622,623],[571,4330,671],{"className":4331},[700],[571,4333],{"className":4334,"style":945},[627],[571,4336,818],{"className":4337},[949],[571,4339],{"className":4340,"style":945},[627],[571,4342,4344,4347],{"className":4343},[613],[571,4345],{"className":4346,"style":642},[617],[571,4348,850],{"className":4349},[622,623],[571,4351,4353,4377],{"className":4352},[574],[571,4354,4356],{"className":4355},[578],[580,4357,4358],{"xmlns":582},[584,4359,4360,4374],{},[587,4361,4362,4364,4366,4368,4370,4372],{},[594,4363,1281],{"stretchy":664},[594,4365,596],{},[823,4367,825],{},[594,4369,1286],{"separator":609},[823,4371,825],{},[594,4373,1291],{"stretchy":664},[601,4375,4376],{"encoding":603},"[-1, 1]",[571,4378,4380],{"className":4379,"ariaHidden":609},[608],[571,4381,4383,4386,4389,4392,4395,4398,4401,4404],{"className":4382},[613],[571,4384],{"className":4385,"style":684},[617],[571,4387,1281],{"className":4388},[692],[571,4390,596],{"className":4391},[622],[571,4393,825],{"className":4394},[622],[571,4396,1286],{"className":4397},[1313],[571,4399],{"className":4400,"style":1045},[627],[571,4402,825],{"className":4403},[622],[571,4405,1291],{"className":4406},[700]," ist ",[571,4409,4411,4437],{"className":4410},[574],[571,4412,4414],{"className":4413},[578],[580,4415,4416],{"xmlns":582},[584,4417,4418,4434],{},[587,4419,4420,4422,4424,4426,4428,4430,4432],{},[594,4421,839],{},[590,4423,1344],{},[854,4425,856],{},[590,4427,859],{},[590,4429,850],{},[594,4431,818],{},[823,4433,1432],{},[601,4435,4436],{"encoding":603},"\\int g\\,dx = 0",[571,4438,4440,4474],{"className":4439,"ariaHidden":609},[608],[571,4441,4443,4447,4450,4453,4456,4459,4462,4465,4468,4471],{"className":4442},[613],[571,4444],{"className":4445,"style":4446},[617],"height:1.1111em;vertical-align:-0.3061em;",[571,4448,839],{"className":4449,"style":2152},[1049,1053,2151],[571,4451],{"className":4452,"style":1045},[627],[571,4454,1344],{"className":4455,"style":1360},[622,623],[571,4457],{"className":4458,"style":1045},[627],[571,4460,859],{"className":4461},[622,623],[571,4463,850],{"className":4464},[622,623],[571,4466],{"className":4467,"style":945},[627],[571,4469,818],{"className":4470},[949],[571,4472],{"className":4473,"style":945},[627],[571,4475,4477,4480],{"className":4476},[613],[571,4478],{"className":4479,"style":1464},[617],[571,4481,1432],{"className":4482},[622],". Mit ",[571,4485,4487,4511],{"className":4486},[574],[571,4488,4490],{"className":4489},[578],[580,4491,4492],{"xmlns":582},[584,4493,4494,4508],{},[587,4495,4496,4498,4500,4502,4504,4506],{},[590,4497,661],{},[594,4499,665],{"stretchy":664},[590,4501,850],{},[594,4503,671],{"stretchy":664},[594,4505,818],{},[590,4507,850],{},[601,4509,4510],{"encoding":603},"f(x) = 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