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人気のある微分積分 >

integral from 0 to pi of 20sin^4(x)

解

\int_{0}^{π} 20 sin^{4} (x) d x

解

\frac{15 π}{2}

+1

十進法表記

23.56194 \dots

解答ステップ

\int_{0}^{π} 20 sin^{4} (x) d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 20 \cdot \int_{0}^{π} sin^{4} (x) d x

積分換算を適用する

= 20 (- [\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}

= 20 (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2})

簡素化

20 (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2}) : 20 (- [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} + \frac{3 π}{8})

= 20 (- [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} + \frac{3 π}{8})

限度を計算する:

0

= 20 (- 0 + \frac{3 π}{8})

簡素化

= \frac{15 π}{2}

グラフ

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