integral from 1 to 4 of sqrt(6/x)

解答

\int_{1}^{4} \frac{6}{x} d x

26

十进制

4.89897 \dots

求解步骤

\int_{1}^{4} \frac{6}{x} d x

使用分布积分法

= [\frac{6}{x} x - \int - \frac{3}{2 x ^{\frac{1}{2}}} d x]_{1}^{4}

\int - \frac{3}{2 x ^{\frac{1}{2}}} d x = - 6 x

= [\frac{6}{x} x - (- 6 x)]_{1}^{4}

化简

= [\frac{6}{x} x + 6 x]_{1}^{4}

带入上下限计算后得:

26

= 26

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