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

解

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

\frac{9}{2}

十進法表記

4.5

解答ステップ

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

拡張

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

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

\int_{0}^{3} 3 x d x = \frac{27}{2}

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

= \frac{27}{2} - 9

簡素化

\frac{27}{2} - 9 : \frac{9}{2}

= \frac{9}{2}