integral from 1/3 to 3 of (3-3/(x^2))

解

\int_{\frac{1}{3}}^{3} (3 - \frac{3}{x ^{2}}) d x

0

解答ステップ

\int_{\frac{1}{3}}^{3} 3 - \frac{3}{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_{\frac{1}{3}}^{3} 3 d x - \int_{\frac{1}{3}}^{3} \frac{3}{x ^{2}} d x

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

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

= 8 - 8

簡素化

= 0