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受欢迎的微积分 >

integral from 1 to 2 of 7x^2sqrt(8+x^3)

解答

\int_{1}^{2} 7 x^{2} 8 + x^{3} d x

解答

\frac{518}{9}

+1

十进制

57.55555 \dots

求解步骤

\int_{1}^{2} 7 x^{2} 8 + x^{3} d x

提出常数:

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

= 7 \cdot \int_{1}^{2} x^{2} 8 + x^{3} d x

使用换元积分法

= 7 \cdot \int_{9}^{16} \frac{u}{3} d u

提出常数:

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

= 7 \cdot \frac{1}{3} \cdot \int_{9}^{16} u d u

使用幂法则

= 7 \cdot \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{16}

化简

7 \cdot \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{16} : \frac{7}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{16}

= \frac{7}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{16}

带入上下限计算后得:

\frac{74}{3}

= \frac{7}{3} \cdot \frac{74}{3}

化简

= \frac{518}{9}

作图

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