miniaufgabe.js
==== 25. März 2019 bis 29. März 2019 ====
=== Mittwoch 27. März 2019 ===
Bestimmen Sie folgende Stammfunktionen
miniAufgabe("#exoStammfunktionenbestimmen","#solStammfunktionenbestimmen",
[["a) $\\displaystyle \\int \\frac{2}{3}\\sqrt{x} \\, \\mathrm{d} x$ $\\quad$ b) $\\displaystyle \\int -\\frac{5}{3}\\cdot \\frac{1}{x^{2}} \\, \\mathrm{d} x$ $\\quad$ c) $\\displaystyle \\int -\\frac{1}{3}\\cdot \\frac{1}{x} \\, \\mathrm{d} x$", "a) $\\displaystyle \\frac{4}{9}x^{\\frac{3}{2}}+C$ $\\quad$ b) $\\displaystyle \\frac{5}{3}\\cdot \\frac{1}{x^{1}}+C$ $\\quad$ c) $\\displaystyle -\\frac{1}{3}\\cdot \\ln(x)+C$"], ["a) $\\displaystyle \\int -\\frac{5}{6}\\cdot \\mathrm{e}^x \\, \\mathrm{d} x$ $\\quad$ b) $\\displaystyle \\int -\\frac{5}{4}\\sqrt[3]{x} \\, \\mathrm{d} x$ $\\quad$ c) $\\displaystyle \\int \\frac{9}{13}\\cdot \\frac{1}{x^{5}} \\, \\mathrm{d} x$", "a) $\\displaystyle -\\frac{5}{6}\\cdot \\mathrm{e}^x+C$ $\\quad$ b) $\\displaystyle -\\frac{15}{16}x^{\\frac{4}{3}}+C$ $\\quad$ c) $\\displaystyle -\\frac{9}{52}\\cdot \\frac{1}{x^{4}}+C$"], ["a) $\\displaystyle \\int \\frac{7}{10}\\sqrt{x} \\, \\mathrm{d} x$ $\\quad$ b) $\\displaystyle \\int -\\frac{6}{13}\\cdot \\frac{1}{x} \\, \\mathrm{d} x$ $\\quad$ c) $\\displaystyle \\int \\frac{5}{4}\\cdot \\mathrm{e}^x \\, \\mathrm{d} x$", "a) $\\displaystyle \\frac{7}{15}x^{\\frac{3}{2}}+C$ $\\quad$ b) $\\displaystyle -\\frac{6}{13}\\cdot \\ln(x)+C$ $\\quad$ c) $\\displaystyle \\frac{5}{4}\\cdot \\mathrm{e}^x+C$"], ["a) $\\displaystyle \\int \\frac{10}{3}\\sqrt[5]{x} \\, \\mathrm{d} x$ $\\quad$ b) $\\displaystyle \\int \\frac{3}{4}\\cdot \\frac{1}{x^{3}} \\, \\mathrm{d} x$ $\\quad$ c) $\\displaystyle \\int -\\frac{5}{7}\\cdot \\frac{1}{x} \\, \\mathrm{d} x$", "a) $\\displaystyle \\frac{25}{9}x^{\\frac{6}{5}}+C$ $\\quad$ b) $\\displaystyle -\\frac{3}{8}\\cdot \\frac{1}{x^{2}}+C$ $\\quad$ c) $\\displaystyle -\\frac{5}{7}\\cdot \\ln(x)+C$"], ["a) $\\displaystyle \\int -\\frac{2}{5}\\cos(x) \\, \\mathrm{d} x$ $\\quad$ b) $\\displaystyle \\int -\\frac{3}{4}\\sqrt[4]{x} \\, \\mathrm{d} x$ $\\quad$ c) $\\displaystyle \\int -\\frac{9}{11}\\cdot \\mathrm{e}^x \\, \\mathrm{d} x$", "a) $\\displaystyle -\\frac{2}{5}\\sin(x)+C$ $\\quad$ b) $\\displaystyle -\\frac{3}{5}x^{\\frac{5}{4}}+C$ $\\quad$ c) $\\displaystyle -\\frac{9}{11}\\cdot \\mathrm{e}^x+C$"], ["a) $\\displaystyle \\int \\frac{4}{7}\\cdot \\frac{1}{x} \\, \\mathrm{d} x$ $\\quad$ b) $\\displaystyle \\int -\\frac{4}{7}\\cdot \\mathrm{e}^x \\, \\mathrm{d} x$ $\\quad$ c) $\\displaystyle \\int \\frac{9}{10}\\cos(x) \\, \\mathrm{d} x$", "a) $\\displaystyle \\frac{4}{7}\\cdot \\ln(x)+C$ $\\quad$ b) $\\displaystyle -\\frac{4}{7}\\cdot \\mathrm{e}^x+C$ $\\quad$ c) $\\displaystyle \\frac{9}{10}\\sin(x)+C$"], ["a) $\\displaystyle \\int \\frac{3}{4}\\cdot \\frac{1}{x} \\, \\mathrm{d} x$ $\\quad$ b) $\\displaystyle \\int \\frac{5}{8}\\cdot \\frac{1}{x^{2}} \\, \\mathrm{d} x$ $\\quad$ c) $\\displaystyle \\int -\\frac{5}{13}\\sqrt[4]{x} \\, \\mathrm{d} x$", "a) $\\displaystyle \\frac{3}{4}\\cdot \\ln(x)+C$ $\\quad$ b) $\\displaystyle -\\frac{5}{8}\\cdot \\frac{1}{x^{1}}+C$ $\\quad$ c) $\\displaystyle -\\frac{4}{13}x^{\\frac{5}{4}}+C$"], ["a) $\\displaystyle \\int -\\frac{5}{3}\\cdot \\frac{1}{x^{3}} \\, \\mathrm{d} x$ $\\quad$ b) $\\displaystyle \\int \\frac{10}{9}\\cdot \\mathrm{e}^x \\, \\mathrm{d} x$ $\\quad$ c) $\\displaystyle \\int \\frac{4}{5}\\cdot \\frac{1}{x} \\, \\mathrm{d} x$", "a) $\\displaystyle \\frac{5}{6}\\cdot \\frac{1}{x^{2}}+C$ $\\quad$ b) $\\displaystyle \\frac{10}{9}\\cdot \\mathrm{e}^x+C$ $\\quad$ c) $\\displaystyle \\frac{4}{5}\\cdot \\ln(x)+C$"], ["a) $\\displaystyle \\int \\frac{9}{4}\\cdot \\frac{1}{x^{3}} \\, \\mathrm{d} x$ $\\quad$ b) $\\displaystyle \\int \\frac{1}{3}\\cdot \\mathrm{e}^x \\, \\mathrm{d} x$ $\\quad$ c) $\\displaystyle \\int -\\frac{3}{5}\\cdot \\frac{1}{x} \\, \\mathrm{d} x$", "a) $\\displaystyle -\\frac{9}{8}\\cdot \\frac{1}{x^{2}}+C$ $\\quad$ b) $\\displaystyle \\frac{1}{3}\\cdot \\mathrm{e}^x+C$ $\\quad$ c) $\\displaystyle -\\frac{3}{5}\\cdot \\ln(x)+C$"], ["a) $\\displaystyle \\int \\frac{9}{11}\\cdot \\frac{1}{x} \\, \\mathrm{d} x$ $\\quad$ b) $\\displaystyle \\int \\frac{2}{3}\\cdot \\mathrm{e}^x \\, \\mathrm{d} x$ $\\quad$ c) $\\displaystyle \\int \\frac{8}{5}\\sin(x) \\, \\mathrm{d} x$", "a) $\\displaystyle \\frac{9}{11}\\cdot \\ln(x)+C$ $\\quad$ b) $\\displaystyle \\frac{2}{3}\\cdot \\mathrm{e}^x+C$ $\\quad$ c) $\\displaystyle -\\frac{8}{5}\\cos(x)+C$"]],
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=== Freitag 29. März 2019 ===
Berechnen Sie
miniAufgabe("#exobestimmteintpotenzfunktion","#solbestimmteintpotenzfunktion",
[["$\\displaystyle \\int_{\\sqrt[21]{2}}^{\\sqrt[21]{5}} \\frac{7}{10} \\cdot x^{\\frac{10}{11}} \\, \\textrm{d} x$", "$\\displaystyle \\frac{7}{10} \\cdot \\int_{\\sqrt[21]{2}}^{\\sqrt[21]{5}} x^{\\frac{10}{11}} \\, \\textrm{d} x = \\frac{7}{10} \\cdot \\left(\\frac{11}{21}\\cdot x^{\\frac{21}{11}} \\right) \\Bigg|_{\\sqrt[21]{2}}^{\\sqrt[21]{5}} = \\frac{7}{10} \\cdot \\left(\\frac{11}{21}\\cdot \\left(5^{\\frac{1}{21}}\\right)^{\\frac{21}{11}} - \\frac{11}{21}\\cdot \\left(2^{\\frac{1}{21}}\\right)^{\\frac{21}{11}}\\right) = \\frac{7}{10} \\cdot \\frac{11}{21} \\cdot \\left(\\sqrt[11]{5} - \\sqrt[11]{2}\\right) = \\frac{11}{30}\\cdot \\left(\\sqrt[11]{5} - \\sqrt[11]{2}\\right)$"], ["$\\displaystyle \\int_{\\sqrt[7]{2}}^{\\sqrt[7]{3}} -\\frac{7}{12} \\cdot x^{\\frac{4}{3}} \\, \\textrm{d} x$", "$\\displaystyle -\\frac{7}{12} \\cdot \\int_{\\sqrt[7]{2}}^{\\sqrt[7]{3}} x^{\\frac{4}{3}} \\, \\textrm{d} x = -\\frac{7}{12} \\cdot \\left(\\frac{3}{7}\\cdot x^{\\frac{7}{3}} \\right) \\Bigg|_{\\sqrt[7]{2}}^{\\sqrt[7]{3}} = -\\frac{7}{12} \\cdot \\left(\\frac{3}{7}\\cdot \\left(3^{\\frac{1}{7}}\\right)^{\\frac{7}{3}} - \\frac{3}{7}\\cdot \\left(2^{\\frac{1}{7}}\\right)^{\\frac{7}{3}}\\right) = -\\frac{7}{12} \\cdot \\frac{3}{7} \\cdot \\left(\\sqrt[3]{3} - \\sqrt[3]{2}\\right) = -\\frac{1}{4}\\cdot \\left(\\sqrt[3]{3} - \\sqrt[3]{2}\\right)$"], ["$\\displaystyle \\int_{\\sqrt[16]{5}}^{\\sqrt[16]{6}} \\frac{4}{13} \\cdot x^{\\frac{7}{9}} \\, \\textrm{d} x$", "$\\displaystyle \\frac{4}{13} \\cdot \\int_{\\sqrt[16]{5}}^{\\sqrt[16]{6}} x^{\\frac{7}{9}} \\, \\textrm{d} x = \\frac{4}{13} \\cdot \\left(\\frac{9}{16}\\cdot x^{\\frac{16}{9}} \\right) \\Bigg|_{\\sqrt[16]{5}}^{\\sqrt[16]{6}} = \\frac{4}{13} \\cdot \\left(\\frac{9}{16}\\cdot \\left(6^{\\frac{1}{16}}\\right)^{\\frac{16}{9}} - \\frac{9}{16}\\cdot \\left(5^{\\frac{1}{16}}\\right)^{\\frac{16}{9}}\\right) = \\frac{4}{13} \\cdot \\frac{9}{16} \\cdot \\left(\\sqrt[9]{6} - \\sqrt[9]{5}\\right) = \\frac{9}{52}\\cdot \\left(\\sqrt[9]{6} - \\sqrt[9]{5}\\right)$"], ["$\\displaystyle \\int_{\\sqrt[16]{4}}^{\\sqrt[16]{5}} \\frac{4}{9} \\cdot x^{\\frac{3}{13}} \\, \\textrm{d} x$", "$\\displaystyle \\frac{4}{9} \\cdot \\int_{\\sqrt[16]{4}}^{\\sqrt[16]{5}} x^{\\frac{3}{13}} \\, \\textrm{d} x = \\frac{4}{9} \\cdot \\left(\\frac{13}{16}\\cdot x^{\\frac{16}{13}} \\right) \\Bigg|_{\\sqrt[16]{4}}^{\\sqrt[16]{5}} = \\frac{4}{9} \\cdot \\left(\\frac{13}{16}\\cdot \\left(5^{\\frac{1}{16}}\\right)^{\\frac{16}{13}} - \\frac{13}{16}\\cdot \\left(4^{\\frac{1}{16}}\\right)^{\\frac{16}{13}}\\right) = \\frac{4}{9} \\cdot \\frac{13}{16} \\cdot \\left(\\sqrt[13]{5} - \\sqrt[13]{4}\\right) = \\frac{13}{36}\\cdot \\left(\\sqrt[13]{5} - \\sqrt[13]{4}\\right)$"], ["$\\displaystyle \\int_{\\sqrt[21]{2}}^{\\sqrt[21]{3}} -\\frac{12}{11} \\cdot x^{\\frac{8}{13}} \\, \\textrm{d} x$", "$\\displaystyle -\\frac{12}{11} \\cdot \\int_{\\sqrt[21]{2}}^{\\sqrt[21]{3}} x^{\\frac{8}{13}} \\, \\textrm{d} x = -\\frac{12}{11} \\cdot \\left(\\frac{13}{21}\\cdot x^{\\frac{21}{13}} \\right) \\Bigg|_{\\sqrt[21]{2}}^{\\sqrt[21]{3}} = -\\frac{12}{11} \\cdot \\left(\\frac{13}{21}\\cdot \\left(3^{\\frac{1}{21}}\\right)^{\\frac{21}{13}} - \\frac{13}{21}\\cdot \\left(2^{\\frac{1}{21}}\\right)^{\\frac{21}{13}}\\right) = -\\frac{12}{11} \\cdot \\frac{13}{21} \\cdot \\left(\\sqrt[13]{3} - \\sqrt[13]{2}\\right) = -\\frac{52}{77}\\cdot \\left(\\sqrt[13]{3} - \\sqrt[13]{2}\\right)$"], ["$\\displaystyle \\int_{\\sqrt[2]{2}}^{\\sqrt[2]{3}} -\\frac{11}{10} \\cdot x^{-\\frac{3}{5}} \\, \\textrm{d} x$", "$\\displaystyle -\\frac{11}{10} \\cdot \\int_{\\sqrt[2]{2}}^{\\sqrt[2]{3}} x^{-\\frac{3}{5}} \\, \\textrm{d} x = -\\frac{11}{10} \\cdot \\left(\\frac{5}{2}\\cdot x^{\\frac{2}{5}} \\right) \\Bigg|_{\\sqrt[2]{2}}^{\\sqrt[2]{3}} = -\\frac{11}{10} \\cdot \\left(\\frac{5}{2}\\cdot \\left(3^{\\frac{1}{2}}\\right)^{\\frac{2}{5}} - \\frac{5}{2}\\cdot \\left(2^{\\frac{1}{2}}\\right)^{\\frac{2}{5}}\\right) = -\\frac{11}{10} \\cdot \\frac{5}{2} \\cdot \\left(\\sqrt[5]{3} - \\sqrt[5]{2}\\right) = -\\frac{11}{4}\\cdot \\left(\\sqrt[5]{3} - \\sqrt[5]{2}\\right)$"], ["$\\displaystyle \\int_{\\sqrt[2]{4}}^{\\sqrt[2]{5}} -\\frac{7}{26} \\cdot x^{-\\frac{5}{7}} \\, \\textrm{d} x$", "$\\displaystyle -\\frac{7}{26} \\cdot \\int_{\\sqrt[2]{4}}^{\\sqrt[2]{5}} x^{-\\frac{5}{7}} \\, \\textrm{d} x = -\\frac{7}{26} \\cdot \\left(\\frac{7}{2}\\cdot x^{\\frac{2}{7}} \\right) \\Bigg|_{\\sqrt[2]{4}}^{\\sqrt[2]{5}} = -\\frac{7}{26} \\cdot \\left(\\frac{7}{2}\\cdot \\left(5^{\\frac{1}{2}}\\right)^{\\frac{2}{7}} - \\frac{7}{2}\\cdot \\left(4^{\\frac{1}{2}}\\right)^{\\frac{2}{7}}\\right) = -\\frac{7}{26} \\cdot \\frac{7}{2} \\cdot \\left(\\sqrt[7]{5} - \\sqrt[7]{4}\\right) = -\\frac{49}{52}\\cdot \\left(\\sqrt[7]{5} - \\sqrt[7]{4}\\right)$"], ["$\\displaystyle \\int_{\\sqrt[17]{2}}^{\\sqrt[17]{4}} \\frac{17}{20} \\cdot x^{\\frac{6}{11}} \\, \\textrm{d} x$", "$\\displaystyle \\frac{17}{20} \\cdot \\int_{\\sqrt[17]{2}}^{\\sqrt[17]{4}} x^{\\frac{6}{11}} \\, \\textrm{d} x = \\frac{17}{20} \\cdot \\left(\\frac{11}{17}\\cdot x^{\\frac{17}{11}} \\right) \\Bigg|_{\\sqrt[17]{2}}^{\\sqrt[17]{4}} = \\frac{17}{20} \\cdot \\left(\\frac{11}{17}\\cdot \\left(4^{\\frac{1}{17}}\\right)^{\\frac{17}{11}} - \\frac{11}{17}\\cdot \\left(2^{\\frac{1}{17}}\\right)^{\\frac{17}{11}}\\right) = \\frac{17}{20} \\cdot \\frac{11}{17} \\cdot \\left(\\sqrt[11]{4} - \\sqrt[11]{2}\\right) = \\frac{11}{20}\\cdot \\left(\\sqrt[11]{4} - \\sqrt[11]{2}\\right)$"], ["$\\displaystyle \\int_{\\sqrt[3]{3}}^{\\sqrt[3]{4}} -\\frac{9}{19} \\cdot x^{-\\frac{4}{7}} \\, \\textrm{d} x$", "$\\displaystyle -\\frac{9}{19} \\cdot \\int_{\\sqrt[3]{3}}^{\\sqrt[3]{4}} x^{-\\frac{4}{7}} \\, \\textrm{d} x = -\\frac{9}{19} \\cdot \\left(\\frac{7}{3}\\cdot x^{\\frac{3}{7}} \\right) \\Bigg|_{\\sqrt[3]{3}}^{\\sqrt[3]{4}} = -\\frac{9}{19} \\cdot \\left(\\frac{7}{3}\\cdot \\left(4^{\\frac{1}{3}}\\right)^{\\frac{3}{7}} - \\frac{7}{3}\\cdot \\left(3^{\\frac{1}{3}}\\right)^{\\frac{3}{7}}\\right) = -\\frac{9}{19} \\cdot \\frac{7}{3} \\cdot \\left(\\sqrt[7]{4} - \\sqrt[7]{3}\\right) = -\\frac{21}{19}\\cdot \\left(\\sqrt[7]{4} - \\sqrt[7]{3}\\right)$"], ["$\\displaystyle \\int_{\\sqrt[9]{5}}^{\\sqrt[9]{6}} \\frac{5}{11} \\cdot x^{\\frac{5}{4}} \\, \\textrm{d} x$", "$\\displaystyle \\frac{5}{11} \\cdot \\int_{\\sqrt[9]{5}}^{\\sqrt[9]{6}} x^{\\frac{5}{4}} \\, \\textrm{d} x = \\frac{5}{11} \\cdot \\left(\\frac{4}{9}\\cdot x^{\\frac{9}{4}} \\right) \\Bigg|_{\\sqrt[9]{5}}^{\\sqrt[9]{6}} = \\frac{5}{11} \\cdot \\left(\\frac{4}{9}\\cdot \\left(6^{\\frac{1}{9}}\\right)^{\\frac{9}{4}} - \\frac{4}{9}\\cdot \\left(5^{\\frac{1}{9}}\\right)^{\\frac{9}{4}}\\right) = \\frac{5}{11} \\cdot \\frac{4}{9} \\cdot \\left(\\sqrt[4]{6} - \\sqrt[4]{5}\\right) = \\frac{20}{99}\\cdot \\left(\\sqrt[4]{6} - \\sqrt[4]{5}\\right)$"]],
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