integral from 0 to pi of (2x-1)cos(5x)

解答

\int_{0}^{π} (2 x - 1) cos (5 x) d x

- \frac{4}{25}

十进制

- 0.16

求解步骤

\int_{0}^{π} (2 x - 1) cos (5 x) d x

乘开

(2 x - 1) cos (5 x) : 2 x cos (5 x) - cos (5 x)

= \int_{0}^{π} 2 x cos (5 x) - cos (5 x) d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{π} 2 x cos (5 x) d x - \int_{0}^{π} cos (5 x) d x

\int_{0}^{π} 2 x cos (5 x) d x = - \frac{4}{25}

\int_{0}^{π} cos (5 x) d x = 0

= - \frac{4}{25} - 0

化简

= - \frac{4}{25}

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