integral from 0 to 2 of (9-x)sqrt(x)

解

\int_{0}^{2} (9 - x) x d x

122 - \frac{8 2}{5}

十進法表記

14.70782 \dots

解答ステップ

\int_{0}^{2} (9 - x) x d x

拡張

(9 - x) x : 9 x - x^{\frac{3}{2}}

= \int_{0}^{2} 9 x - x^{\frac{3}{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_{0}^{2} 9 x d x - \int_{0}^{2} x^{\frac{3}{2}} d x

\int_{0}^{2} 9 x d x = 122

\int_{0}^{2} x^{\frac{3}{2}} d x = \frac{8 2}{5}

= 122 - \frac{8 2}{5}