integral from 1 to 4 of 4/x-(16)/(x^2)

解

\int_{1}^{4} \frac{4}{x} - \frac{16}{x ^{2}} d x

8 ln (2) - 12

十進法表記

- 6.45482 \dots

解答ステップ

\int_{1}^{4} \frac{4}{x} - \frac{16}{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}^{4} \frac{4}{x} d x - \int_{1}^{4} \frac{16}{x ^{2}} d x

\int_{1}^{4} \frac{4}{x} d x = 8 ln (2)

\int_{1}^{4} \frac{16}{x ^{2}} d x = 12

= 8 ln (2) - 12