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

解

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

ln (2) - \frac{3}{8}

十進法表記

0.31814 \dots

解答ステップ

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

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

\int_{1}^{2} \frac{x}{4} d x = \frac{3}{8}

= ln (2) - \frac{3}{8}