integral from 1 to 4 of (x/2-2/x)

解答

\int_{1}^{4} (\frac{x}{2} - \frac{2}{x}) d x

\frac{15}{4} - 4 ln (2)

十进制

0.97741 \dots

求解步骤

\int_{1}^{4} \frac{x}{2} - \frac{2}{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_{1}^{4} \frac{x}{2} d x - \int_{1}^{4} \frac{2}{x} d x

\int_{1}^{4} \frac{x}{2} d x = \frac{15}{4}

\int_{1}^{4} \frac{2}{x} d x = 4 ln (2)

= \frac{15}{4} - 4 ln (2)