5.3 The Fundamental Theorem of Calculus/23: Difference between revisions
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\int_{0}^{1}x^{\frac{4}{5}}dx &=\frac{x^{\frac{4}{5}+1}}{\frac{4}{5}+1} \bigg|_{0}^{1} =\frac{x^{\frac{9}{5}}}{\frac{9}{5}} \bigg|_{0}^{1} \\[2ex] | \int_{0}^{1}x^{\frac{4}{5}}dx &=\frac{x^{\frac{4}{5}+1}}{\frac{4}{5}+1} \bigg|_{0}^{1} =\frac{x^{\frac{9}{5}}}{\frac{9}{5}} \bigg|_{0}^{1} \\[2ex] | ||
&=\frac{5\sqrt[5]{1^9}}{9}-\frac{5 \sqrt[5]{0^9}}{9} \\[2ex] | &=\frac{5\sqrt[5]{(1)^9}}{9}-\frac{5 \sqrt[5]{(0)^9}}{9} \\[2ex] | ||
&=\cfrac{5}{9} | &=\cfrac{5}{9} | ||
Revision as of 20:50, 6 September 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int _{0}^{1}x^{\frac {4}{5}}dx&={\frac {x^{{\frac {4}{5}}+1}}{{\frac {4}{5}}+1}}{\bigg |}_{0}^{1}={\frac {x^{\frac {9}{5}}}{\frac {9}{5}}}{\bigg |}_{0}^{1}\\[2ex]&={\frac {5{\sqrt[{5}]{(1)^{9}}}}{9}}-{\frac {5{\sqrt[{5}]{(0)^{9}}}}{9}}\\[2ex]&={\cfrac {5}{9}}\end{aligned}}}