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受欢迎的微积分 >

integral from 2 to 4 of-0.0008xe^{x^2}

解答

\int_{2}^{4} - 0.0008 x e^{x^{2}} d x

解答

- 3554.42236 \dots

求解步骤

\int_{2}^{4} - 0.0008 x e^{x^{2}} d x

提出常数:

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

= - 0.0008 \cdot \int_{2}^{4} x e^{x^{2}} d x

使用换元积分法

= - 0.0008 \cdot \int_{4}^{16} \frac{e ^{u}}{2} d u

提出常数:

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

= - 0.0008 \cdot \frac{1}{2} \cdot \int_{4}^{16} e^{u} d u

使用积分常见定则:

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

= - 0.0008 \cdot \frac{1}{2} [e^{u}]_{4}^{16}

化简

- 0.0008 \cdot \frac{1}{2} [e^{u}]_{4}^{16} : - 0.0004 [e^{u}]_{4}^{16}

= - 0.0004 [e^{u}]_{4}^{16}

带入上下限计算后得:

e^{16} - e^{4}

= - 0.0004 (e^{16} - e^{4})

化简

= - 3554.42236 \dots

作图

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