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

解

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

- \frac{34}{3}

十進法表記

- 11.33333 \dots

解答ステップ

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

拡張

(x + 2) (x - 3) : x^{2} - x - 6

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

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

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

\int_{0}^{2} 6 d x = 12

= \frac{8}{3} - 2 - 12

簡素化

\frac{8}{3} - 2 - 12 : - \frac{34}{3}

= - \frac{34}{3}