integral from 1 to 8 of (x/8-6/x)

解

\int_{1}^{8} (\frac{x}{8} - \frac{6}{x}) d x

\frac{63}{16} - 18 ln (2)

十進法表記

- 8.53914 \dots

解答ステップ

\int_{1}^{8} \frac{x}{8} - \frac{6}{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_{1}^{8} \frac{x}{8} d x - \int_{1}^{8} \frac{6}{x} d x

\int_{1}^{8} \frac{x}{8} d x = \frac{63}{16}

\int_{1}^{8} \frac{6}{x} d x = 18 ln (2)

= \frac{63}{16} - 18 ln (2)