integral from 1/2 to 6 of 3/x-1/12 x

解答

\int_{\frac{1}{2}}^{6} \frac{3}{x} - \frac{1}{12} x d x

3 ln (12) - \frac{143}{96}

十进制

5.96513 \dots

求解步骤

\int_{\frac{1}{2}}^{6} \frac{3}{x} - \frac{1}{12} x d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{\frac{1}{2}}^{6} \frac{3}{x} d x - \int_{\frac{1}{2}}^{6} \frac{1}{12} x d x

\int_{\frac{1}{2}}^{6} \frac{3}{x} d x = 3 ln (12)

\int_{\frac{1}{2}}^{6} \frac{1}{12} x d x = \frac{143}{96}

= 3 ln (12) - \frac{143}{96}

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