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受欢迎的微积分 >

integral from 1 to 2 of 2x^2sqrt(x^3+6)

解答

\int_{1}^{2} 2 x^{2} x^{3} + 6 d x

解答

\frac{2 ( 28 14 - 14 7 )}{9}

+1

十进制

15.05019 \dots

求解步骤

\int_{1}^{2} 2 x^{2} x^{3} + 6 d x

提出常数:

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

= 2 \cdot \int_{1}^{2} x^{2} x^{3} + 6 d x

使用换元积分法

= 2 \cdot \int_{7}^{14} \frac{u}{3} d u

提出常数:

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

= 2 \cdot \frac{1}{3} \cdot \int_{7}^{14} u d u

使用幂法则

= 2 \cdot \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{14}

化简

2 \cdot \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{14} : \frac{2}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{14}

= \frac{2}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{14}

带入上下限计算后得:

\frac{28 14 - 14 7}{3}

= \frac{2}{3} \cdot \frac{28 14 - 14 7}{3}

化简

= \frac{2 ( 28 14 - 14 7 )}{9}

作图

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