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人気のある微分積分 >

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

解

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

解

- 1

解答ステップ

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

定数を除く:

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

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

u置換積分法を適用する

= 2 \cdot \int_{0}^{π} \frac{u cos ( u )}{4} d u

定数を除く:

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

= 2 \cdot \frac{1}{4} \cdot \int_{0}^{π} u cos (u) d u

部分積分を適用する

= 2 \cdot \frac{1}{4} [u sin (u) - \int sin (u) d u]_{0}^{π}

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

= 2 \cdot \frac{1}{4} [u sin (u) - (- cos (u))]_{0}^{π}

簡素化

2 \cdot \frac{1}{4} [u sin (u) - (- cos (u))]_{0}^{π} : \frac{1}{2} [u sin (u) + cos (u)]_{0}^{π}

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

限度を計算する:

- 2

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

簡素化

= - 1

グラフ

人気の例

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