integral from-2 to 0 of (x-3)(x+5)

解

\int_{- 2}^{0} (x - 3) (x + 5) d x

- \frac{94}{3}

十進法表記

- 31.33333 \dots

解答ステップ

\int_{- 2}^{0} (x - 3) (x + 5) d x

拡張

(x - 3) (x + 5) : x^{2} + 2 x - 15

= \int_{- 2}^{0} x^{2} + 2 x - 15 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_{- 2}^{0} x^{2} d x + \int_{- 2}^{0} 2 x d x - \int_{- 2}^{0} 15 d x

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

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

\int_{- 2}^{0} 15 d x = 30

= \frac{8}{3} - 4 - 30

簡素化

\frac{8}{3} - 4 - 30 : - \frac{94}{3}

= - \frac{94}{3}