integral from 0 to 3pi of xsin(x)

解答

\int_{0}^{3 π} x sin (x) d x

3 π

十进制

9.42477 \dots

求解步骤

\int_{0}^{3 π} x sin (x) d x

使用分布积分法

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

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

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

化简

= [- x cos (x) + sin (x)]_{0}^{3 π}

带入上下限计算后得:

3 π

= 3 π

\int_{1}^{4} x e^{x} d x

\int_{0}^{9} (81 - x^{2}) d x

\int_{- 1}^{0} (x + 4) cos (nπ x) d x

\int_{0}^{2} x^{2} x^{3} + 5 d x

\int_{0}^{1} ln ∣ 1 - x ∣ d x