integral from 2 to 5 of (x-4)^2

解

\int_{2}^{5} (x - 4)^{2} d x

3

解答ステップ

\int_{2}^{5} (x - 4)^{2} d x

拡張

(x - 4)^{2} : x^{2} - 8 x + 16

= \int_{2}^{5} x^{2} - 8 x + 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}^{5} x^{2} d x - \int_{2}^{5} 8 x d x + \int_{2}^{5} 16 d x

\int_{2}^{5} x^{2} d x = 39

\int_{2}^{5} 8 x d x = 84

\int_{2}^{5} 16 d x = 48

= 39 - 84 + 48

簡素化

= 3