integral from 1 to 2 of (10-3x)/(x^3)

解

\int_{1}^{2} \frac{10 - 3 x}{x ^{3}} d x

\frac{9}{4}

十進法表記

2.25

解答ステップ

\int_{1}^{2} \frac{10 - 3 x}{x ^{3}} d x

拡張

\frac{10 - 3 x}{x ^{3}} : \frac{10}{x ^{3}} - \frac{3}{x ^{2}}

= \int_{1}^{2} \frac{10}{x ^{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_{1}^{2} \frac{10}{x ^{3}} d x - \int_{1}^{2} \frac{3}{x ^{2}} d x

\int_{1}^{2} \frac{10}{x ^{3}} d x = \frac{15}{4}

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

= \frac{15}{4} - \frac{3}{2}

簡素化

\frac{15}{4} - \frac{3}{2} : \frac{9}{4}

= \frac{9}{4}