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人気のある微分積分 >

integral from 0 to pi/2 of (sin(x))^6

解

\int_{0}^{\frac{π}{2}} (sin (x))^{6} d x

解

\frac{5 π}{32}

+1

十進法表記

0.49087 \dots

解答ステップ

\int_{0}^{\frac{π}{2}} (sin (x))^{6} d x

簡素化

= \int_{0}^{\frac{π}{2}} sin^{6} (x) d x

積分換算を適用する

= - [\frac{cos ( x ) sin ^{5} ( x )}{6}]_{0}^{\frac{π}{2}} + \frac{5}{6} \cdot \int_{0}^{\frac{π}{2}} sin^{4} (x) d x

\int_{0}^{\frac{π}{2}} sin^{4} (x) d x = \frac{3 π}{16}

= - [\frac{cos ( x ) sin ^{5} ( x )}{6}]_{0}^{\frac{π}{2}} + \frac{5}{6} \cdot \frac{3 π}{16}

簡素化

- [\frac{cos ( x ) sin ^{5} ( x )}{6}]_{0}^{\frac{π}{2}} + \frac{5}{6} \cdot \frac{3 π}{16} : - [\frac{1}{6} sin^{5} (x) cos (x)]_{0}^{\frac{π}{2}} + \frac{5 π}{32}

= - [\frac{1}{6} sin^{5} (x) cos (x)]_{0}^{\frac{π}{2}} + \frac{5 π}{32}

限度を計算する:

0

= - 0 + \frac{5 π}{32}

簡素化

= \frac{5 π}{32}

グラフ

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