integral from 7 to 8 of (5/(x^2)-1)

解

\int_{7}^{8} (\frac{5}{x ^{2}} - 1) d x

- \frac{51}{56}

十進法表記

- 0.91071 \dots

解答ステップ

\int_{7}^{8} \frac{5}{x ^{2}} - 1 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_{7}^{8} \frac{5}{x ^{2}} d x - \int_{7}^{8} 1 d x

\int_{7}^{8} \frac{5}{x ^{2}} d x = \frac{5}{56}

\int_{7}^{8} 1 d x = 1

= \frac{5}{56} - 1

簡素化

\frac{5}{56} - 1 : - \frac{51}{56}

= - \frac{51}{56}