integral from 2 to 8 of (2-x)(x-8)

解

\int_{2}^{8} (2 - x) (x - 8) d x

36

解答ステップ

\int_{2}^{8} (2 - x) (x - 8) d x

拡張

(2 - x) (x - 8) : 10 x - x^{2} - 16

= \int_{2}^{8} 10 x - x^{2} - 16 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}^{8} 10 x d x - \int_{2}^{8} x^{2} d x - \int_{2}^{8} 16 d x

\int_{2}^{8} 10 x d x = 300

\int_{2}^{8} x^{2} d x = 168

\int_{2}^{8} 16 d x = 96

= 300 - 168 - 96

簡素化

= 36