integral from 1 to 3 of (2-x)e^x

解答

\int_{1}^{3} (2 - x) e^{x} d x

- 2 e

十进制

- 5.43656 \dots

求解步骤

\int_{1}^{3} (2 - x) e^{x} d x

使用分布积分法

= [e^{x} (2 - x) - \int - e^{x} d x]_{1}^{3}

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

= [e^{x} (2 - x) - (- e^{x})]_{1}^{3}

化简

[e^{x} (2 - x) - (- e^{x})]_{1}^{3} : [- e^{x} x + 3 e^{x}]_{1}^{3}

= [- e^{x} x + 3 e^{x}]_{1}^{3}

带入上下限计算后得:

- 2 e

= - 2 e