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人気のある微分積分 >

integral from 0 to 2pi of sin^8(x)

解

\int_{0}^{2 π} sin^{8} (x) d x

解

\frac{35 π}{64}

+1

十進法表記

1.71805 \dots

解答ステップ

\int_{0}^{2 π} sin^{8} (x) d x

積分換算を適用する

= - [\frac{cos ( x ) sin ^{7} ( x )}{8}]_{0}^{2 π} + \frac{7}{8} \cdot \int_{0}^{2 π} sin^{6} (x) d x

\int_{0}^{2 π} sin^{6} (x) d x = \frac{5 π}{8}

= - [\frac{cos ( x ) sin ^{7} ( x )}{8}]_{0}^{2 π} + \frac{7}{8} \cdot \frac{5 π}{8}

簡素化

- [\frac{cos ( x ) sin ^{7} ( x )}{8}]_{0}^{2 π} + \frac{7}{8} \cdot \frac{5 π}{8} : - [\frac{1}{8} sin^{7} (x) cos (x)]_{0}^{2 π} + \frac{35 π}{64}

= - [\frac{1}{8} sin^{7} (x) cos (x)]_{0}^{2 π} + \frac{35 π}{64}

限度を計算する:

0

= - 0 + \frac{35 π}{64}

簡素化

= \frac{35 π}{64}

グラフ

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