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

解答

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

\frac{3}{4} - 2 ln (2)

十进制

- 0.63629 \dots

求解步骤

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

\int_{1}^{2} \frac{x}{2} d x = \frac{3}{4}

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

= \frac{3}{4} - 2 ln (2)

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