integral from 0 to 3 of (3-x)sqrt(x)

解

\int_{0}^{3} (3 - x) x d x

63 - \frac{18 3}{5}

十進法表記

4.15692 \dots

解答ステップ

\int_{0}^{3} (3 - x) x d x

拡張

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

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

\int_{0}^{3} 3 x d x = 63

\int_{0}^{3} x^{\frac{3}{2}} d x = \frac{18 3}{5}

= 63 - \frac{18 3}{5}