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

解

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

- \frac{7}{3}

十進法表記

- 2.33333 \dots

解答ステップ

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

\int_{2}^{3} \frac{1}{x ^{2}} d x = \frac{1}{6}

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

= \frac{1}{6} - \frac{5}{2}

簡素化

\frac{1}{6} - \frac{5}{2} : - \frac{7}{3}

= - \frac{7}{3}