integral from 1 to 3 of (2-6x)/(x^3)

解

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

- \frac{28}{9}

十進法表記

- 3.11111 \dots

解答ステップ

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

拡張

\frac{2 - 6 x}{x ^{3}} : \frac{2}{x ^{3}} - \frac{6}{x ^{2}}

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

\int_{1}^{3} \frac{2}{x ^{3}} d x = \frac{8}{9}

\int_{1}^{3} \frac{6}{x ^{2}} d x = 4

= \frac{8}{9} - 4

簡素化

\frac{8}{9} - 4 : - \frac{28}{9}

= - \frac{28}{9}