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人気のある微分積分 >

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

解

\int_{0}^{π} cos^{4} (x) 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} cos^{4} (x) d x

簡素化

cos^{4} (x) : cos^{3} (x) cos (x)

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

部分積分を適用する

= [cos^{3} (x) sin (x) - \int - 3 cos^{2} (x) sin^{2} (x) d x]_{0}^{π}

\int - 3 cos^{2} (x) sin^{2} (x) d x = - \frac{3}{8} (x - \frac{1}{4} sin (4 x))

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

簡素化

[cos^{3} (x) sin (x) - (- \frac{3}{8} (x - \frac{1}{4} sin (4 x)))]_{0}^{π} : [\frac{1}{32} (32 cos^{3} (x) sin (x) + 3 (4 x - sin (4 x)))]_{0}^{π}

= [\frac{1}{32} (32 cos^{3} (x) sin (x) + 3 (4 x - sin (4 x)))]_{0}^{π}

限度を計算する:

\frac{3 π}{8}

= \frac{3 π}{8}

グラフ

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