integral from 0 to sqrt(pi of)xsin(x)

解答

\int_{0}^{π} x sin (x) d x

sin (π) - π cos (π)

十进制

1.33474 \dots

求解步骤

\int_{0}^{π} x sin (x) d x

使用分布积分法

= [- x cos (x) - \int - cos (x) d x]_{0}^{π}

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

= [- x cos (x) - (- sin (x))]_{0}^{π}

化简

= [- x cos (x) + sin (x)]_{0}^{π}

带入上下限计算后得:

sin (π) - π cos (π)

= sin (π) - π cos (π)

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