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人気のある微分積分 >

integral from 0 to pi/3 of xcos(3x)

解

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

解

- \frac{2}{9}

+1

十進法表記

- 0.22222 \dots

解答ステップ

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

u置換積分法を適用する

= \int_{0}^{π} \frac{u cos ( u )}{9} d u

定数を除く:

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

= \frac{1}{9} \cdot \int_{0}^{π} u cos (u) d u

部分積分を適用する

= \frac{1}{9} [u sin (u) - \int sin (u) d u]_{0}^{π}

\int sin (u) d u = - cos (u)

= \frac{1}{9} [u sin (u) - (- cos (u))]_{0}^{π}

簡素化

= \frac{1}{9} [u sin (u) + cos (u)]_{0}^{π}

限度を計算する:

- 2

= \frac{1}{9} (- 2)

簡素化

= - \frac{2}{9}

グラフ

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