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

解

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

4 ln (2) - \frac{15}{16}

十進法表記

1.83508 \dots

解答ステップ

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

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

\int_{\frac{1}{2}}^{2} \frac{1}{2} x d x = \frac{15}{16}

= 4 ln (2) - \frac{15}{16}