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受欢迎的微积分 >

integral from-1 to 2 of x^2e^{x^3+1}

解答

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

解答

\frac{e ^{9} - 1}{3}

+1

十进制

2700.69464 \dots

求解步骤

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

使用换元积分法

= \int_{0}^{9} \frac{e ^{u}}{3} d u

提出常数:

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

= \frac{1}{3} \cdot \int_{0}^{9} e^{u} d u

使用积分常见定则:

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

= \frac{1}{3} [e^{u}]_{0}^{9}

带入上下限计算后得:

e^{9} - 1

= \frac{1}{3} (e^{9} - 1)

化简

= \frac{e ^{9} - 1}{3}

作图

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