integral from 1 to 9 of sqrt((11)/x)

解答

\int_{1}^{9} \frac{11}{x} d x

411

十进制

13.26649 \dots

求解步骤

\int_{1}^{9} \frac{11}{x} d x

使用分布积分法

= [\frac{11}{x} x - \int - \frac{11}{2 x ^{\frac{1}{2}}} d x]_{1}^{9}

\int - \frac{11}{2 x ^{\frac{1}{2}}} d x = - 11 x

= [\frac{11}{x} x - (- 11 x)]_{1}^{9}

化简

= [\frac{11}{x} x + 11 x]_{1}^{9}

带入上下限计算后得:

411

= 411

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