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受欢迎的微积分 >

integral from-3 to-2 of 2x(4-x^2)^3

解答

\int_{- 3}^{- 2} 2 x (4 - x^{2})^{3} d x

解答

\frac{625}{4}

+1

十进制

156.25

求解步骤

\int_{- 3}^{- 2} 2 x (4 - x^{2})^{3} d x

提出常数:

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

= 2 \cdot \int_{- 3}^{- 2} x (4 - x^{2})^{3} d x

使用换元积分法

= 2 \cdot \int_{- 5}^{0} - \frac{u ^{3}}{2} d u

提出常数:

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

= 2 (- \frac{1}{2} \cdot \int_{- 5}^{0} u^{3} d u)

使用幂法则

= 2 (- \frac{1}{2} [\frac{u ^{4}}{4}]_{- 5}^{0})

化简

2 (- \frac{1}{2} [\frac{u ^{4}}{4}]_{- 5}^{0}) : - [\frac{u ^{4}}{4}]_{- 5}^{0}

= - [\frac{u ^{4}}{4}]_{- 5}^{0}

带入上下限计算后得:

- \frac{625}{4}

= - (- \frac{625}{4})

化简

= \frac{625}{4}

作图

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