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人気のある微分積分 >

integral from 0 to pi/2 of xcos(7x)

解

\int_{0}^{\frac{π}{2}} x cos (7 x) d x

解

\frac{- 7 π - 2}{98}

+1

十進法表記

- 0.24480 \dots

解答ステップ

\int_{0}^{\frac{π}{2}} x cos (7 x) d x

u置換積分法を適用する

= \int_{0}^{\frac{7 π}{2}} \frac{u cos ( u )}{49} d u

定数を除く:

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

= \frac{1}{49} \cdot \int_{0}^{\frac{7 π}{2}} u cos (u) d u

部分積分を適用する

= \frac{1}{49} [u sin (u) - \int sin (u) d u]_{0}^{\frac{7 π}{2}}

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

= \frac{1}{49} [u sin (u) - (- cos (u))]_{0}^{\frac{7 π}{2}}

簡素化

= \frac{1}{49} [u sin (u) + cos (u)]_{0}^{\frac{7 π}{2}}

限度を計算する:

- \frac{7 π}{2} - 1

= \frac{1}{49} (- \frac{7 π}{2} - 1)

簡素化

= \frac{- 7 π - 2}{98}

グラフ

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