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人気のある微分積分 >

integral from 0 to pi of (sin(x))^4

解

\int_{0}^{π} (sin (x))^{4} d x

解

\frac{3 π}{8}

+1

十進法表記

1.17809 \dots

解答ステップ

\int_{0}^{π} (sin (x))^{4} d x

簡素化

= \int_{0}^{π} sin^{4} (x) d x

積分換算を適用する

= - [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \int_{0}^{π} sin^{2} (x) d x

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

= - [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2}

簡素化

- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2} : - [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} + \frac{3 π}{8}

= - [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} + \frac{3 π}{8}

限度を計算する:

0

= - 0 + \frac{3 π}{8}

簡素化

= \frac{3 π}{8}

グラフ

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