integral from 0 to 2 of (x^2-2x)

解

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

- \frac{4}{3}

十進法表記

- 1.33333 \dots

解答ステップ

\int_{0}^{2} x^{2} - 2 x 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} x^{2} d x - \int_{0}^{2} 2 x d x

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

\int_{0}^{2} 2 x d x = 4

= \frac{8}{3} - 4

簡素化

\frac{8}{3} - 4 : - \frac{4}{3}

= - \frac{4}{3}