integral from 1/3 to 3 of 5-5/(x^2)

解

\int_{\frac{1}{3}}^{3} 5 - \frac{5}{x ^{2}} d x

0

解答ステップ

\int_{\frac{1}{3}}^{3} 5 - \frac{5}{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} 5 d x - \int_{\frac{1}{3}}^{3} \frac{5}{x ^{2}} d x

\int_{\frac{1}{3}}^{3} 5 d x = \frac{40}{3}

\int_{\frac{1}{3}}^{3} \frac{5}{x ^{2}} d x = \frac{40}{3}

= \frac{40}{3} - \frac{40}{3}

簡素化

= 0