integral from 0 to 1 of 6xe^x

解答

\int_{0}^{1} 6 x e^{x} d x

6

求解步骤

\int_{0}^{1} 6 x e^{x} d x

提出常数:

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

= 6 \cdot \int_{0}^{1} x e^{x} d x

使用分布积分法

= 6 [e^{x} x - \int e^{x} d x]_{0}^{1}

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

= 6 [e^{x} x - e^{x}]_{0}^{1}

带入上下限计算后得:

1

= 6 \cdot 1

化简

= 6

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