integral from 1 to 4 of (x/2-5/x)

解

\int_{1}^{4} (\frac{x}{2} - \frac{5}{x}) d x

\frac{15}{4} - 10 ln (2)

十進法表記

- 3.18147 \dots

解答ステップ

\int_{1}^{4} \frac{x}{2} - \frac{5}{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}^{4} \frac{x}{2} d x - \int_{1}^{4} \frac{5}{x} d x

\int_{1}^{4} \frac{x}{2} d x = \frac{15}{4}

\int_{1}^{4} \frac{5}{x} d x = 10 ln (2)

= \frac{15}{4} - 10 ln (2)