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受欢迎的微积分 >

integral from 0 to pi/5 of xcos(5x)

解答

\int_{0}^{\frac{π}{5}} x cos (5 x) d x

解答

- \frac{2}{25}

+1

十进制

- 0.08

求解步骤

\int_{0}^{\frac{π}{5}} x cos (5 x) d x

使用换元积分法

= \int_{0}^{π} \frac{u cos ( u )}{25} d u

提出常数:

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

= \frac{1}{25} \cdot \int_{0}^{π} u cos (u) d u

使用分布积分法

= \frac{1}{25} [u sin (u) - \int sin (u) d u]_{0}^{π}

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

= \frac{1}{25} [u sin (u) - (- cos (u))]_{0}^{π}

化简

= \frac{1}{25} [u sin (u) + cos (u)]_{0}^{π}

带入上下限计算后得:

- 2

= \frac{1}{25} (- 2)

化简

= - \frac{2}{25}

作图

流行的例子

integral from 0 to 7 of tan(x)

\int_{0}^{7} tan (x) d x

integral from-1 to 2 of (x-1)^2

\int_{- 1}^{2} (x - 1)^{2} d x

integral from 0 to pi/2 of sin(x-y)

\int_{0}^{\frac{π}{2}} sin (x - y) d y

integral from 0 to 1 of x^9e^{-x}

\int_{0}^{1} x^{9} e^{- x} d x

integral from 0 to pi of e^{-x}sin(x)

\int_{0}^{π} e^{- x} sin (x) d x