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受欢迎的微积分 >

integral from 0 to 2 of xe^{4x}

解答

\int_{0}^{2} x e^{4 x} d x

解答

\frac{7 e ^{8} + 1}{16}

+1

十进制

1304.23161 \dots

求解步骤

\int_{0}^{2} x e^{4 x} d x

使用换元积分法

= \int_{0}^{8} \frac{e ^{u} u}{16} d u

提出常数:

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

= \frac{1}{16} \cdot \int_{0}^{8} e^{u} u d u

使用分布积分法

= \frac{1}{16} [e^{u} u - \int e^{u} d u]_{0}^{8}

\int e^{u} d u = e^{u}

= \frac{1}{16} [e^{u} u - e^{u}]_{0}^{8}

带入上下限计算后得:

7 e^{8} + 1

= \frac{1}{16} (7 e^{8} + 1)

化简

= \frac{7 e ^{8} + 1}{16}

作图

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