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

解

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

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

十進法表記

0.63629 \dots

解答ステップ

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

総和規則を適用する:

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

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

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

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

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