integral from-4 to 2 of (12-x-x^2)-(x+4)

解

\int_{- 4}^{2} (12 - x - x^{2}) - (x + 4) d x

36

解答ステップ

\int_{- 4}^{2} 12 - x - x^{2} - (x + 4) d x

簡素化

= \int_{- 4}^{2} - x^{2} - 2 x + 8 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_{- 4}^{2} x^{2} d x - \int_{- 4}^{2} 2 x d x + \int_{- 4}^{2} 8 d x

\int_{- 4}^{2} x^{2} d x = 24

\int_{- 4}^{2} 2 x d x = - 12

\int_{- 4}^{2} 8 d x = 48

= - 24 - (- 12) + 48

簡素化

= 36