integral from-1 to 2 of x(1-x^2)

解

\int_{- 1}^{2} x (1 - x^{2}) d x

- \frac{9}{4}

十進法表記

- 2.25

解答ステップ

\int_{- 1}^{2} x (1 - x^{2}) d x

拡張

x (1 - x^{2}) : x - x^{3}

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

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

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

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

簡素化

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

= - \frac{9}{4}