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受欢迎的微积分 >

integral from 2 to 8 of-sqrt(x/2)

解答

\int_{2}^{8} - \frac{x}{2} d x

解答

- \frac{28}{3}

+1

十进制

- 9.33333 \dots

求解步骤

\int_{2}^{8} - \frac{x}{2} d x

提出常数:

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

= - \int_{2}^{8} \frac{x}{2} d x

化简

\frac{x}{2} : \frac{x}{2}

= - \int_{2}^{8} \frac{x}{2} d x

提出常数:

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

= - \frac{1}{2} \cdot \int_{2}^{8} x d x

使用幂法则

= - \frac{1}{2} [\frac{2}{3} x^{\frac{3}{2}}]_{2}^{8}

带入上下限计算后得:

\frac{28 2}{3}

= - \frac{1}{2} \cdot \frac{28 2}{3}

化简

= - \frac{28}{3}

作图

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