integral from 0 to 2 of (-x^2-3x)

解

\int_{0}^{2} (- x^{2} - 3 x) d x

- \frac{26}{3}

十進法表記

- 8.66666 \dots

解答ステップ

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

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

\int_{0}^{2} 3 x d x = 6

= - \frac{8}{3} - 6

簡素化

- \frac{8}{3} - 6 : - \frac{26}{3}

= - \frac{26}{3}