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人気のある微分積分 >

integral from 0 to pi of 3cos^6(x)

解

\int_{0}^{π} 3 cos^{6} (x) d x

解

\frac{15 π}{16}

+1

十進法表記

2.94524 \dots

解答ステップ

\int_{0}^{π} 3 cos^{6} (x) d x

定数を除く:

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

= 3 \cdot \int_{0}^{π} cos^{6} (x) d x

積分換算を適用する

= 3 ([\frac{sin ( x ) cos ^{5} ( x )}{6}]_{0}^{π} + \frac{5}{6} \cdot \int_{0}^{π} cos^{4} (x) d x)

\int_{0}^{π} cos^{4} (x) d x = \frac{3 π}{8}

= 3 ([\frac{sin ( x ) cos ^{5} ( x )}{6}]_{0}^{π} + \frac{5}{6} \cdot \frac{3 π}{8})

簡素化

3 ([\frac{sin ( x ) cos ^{5} ( x )}{6}]_{0}^{π} + \frac{5}{6} \cdot \frac{3 π}{8}) : 3 ([\frac{1}{6} cos^{5} (x) sin (x)]_{0}^{π} + \frac{5 π}{16})

= 3 ([\frac{1}{6} cos^{5} (x) sin (x)]_{0}^{π} + \frac{5 π}{16})

限度を計算する:

0

= 3 (0 + \frac{5 π}{16})

簡素化

= \frac{15 π}{16}

グラフ

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