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人気のある微分積分 >

integral from 0 to pi/2 of sin^{10}(x)

解

\int_{0}^{\frac{π}{2}} sin^{10} (x) d x

解

\frac{63 π}{512}

+1

十進法表記

0.38656 \dots

解答ステップ

\int_{0}^{\frac{π}{2}} sin^{10} (x) d x

積分換算を適用する

= - [\frac{cos ( x ) sin ^{9} ( x )}{10}]_{0}^{\frac{π}{2}} + \frac{9}{10} \cdot \int_{0}^{\frac{π}{2}} sin^{8} (x) d x

\int_{0}^{\frac{π}{2}} sin^{8} (x) d x = \frac{35 π}{256}

= - [\frac{cos ( x ) sin ^{9} ( x )}{10}]_{0}^{\frac{π}{2}} + \frac{9}{10} \cdot \frac{35 π}{256}

簡素化

- [\frac{cos ( x ) sin ^{9} ( x )}{10}]_{0}^{\frac{π}{2}} + \frac{9}{10} \cdot \frac{35 π}{256} : - [\frac{1}{10} sin^{9} (x) cos (x)]_{0}^{\frac{π}{2}} + \frac{63 π}{512}

= - [\frac{1}{10} sin^{9} (x) cos (x)]_{0}^{\frac{π}{2}} + \frac{63 π}{512}

限度を計算する:

0

= - 0 + \frac{63 π}{512}

簡素化

= \frac{63 π}{512}

グラフ

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