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人気のある微分積分 >

integral from 0 to pi/3 of 2xcos(x)

解

\int_{0}^{\frac{π}{3}} 2 x cos (x) d x

解

- 1 + \frac{π}{3}

+1

十進法表記

0.81379 \dots

解答ステップ

\int_{0}^{\frac{π}{3}} 2 x cos (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}{3}} x cos (x) d x

部分積分を適用する

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

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

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

簡素化

= 2 [x sin (x) + cos (x)]_{0}^{\frac{π}{3}}

限度を計算する:

- \frac{1}{2} + \frac{π}{2 3}

= 2 (- \frac{1}{2} + \frac{π}{2 3})

簡素化

= - 1 + \frac{π}{3}

グラフ

人気の例

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