integral from 4 to 7 of (x-5)^2

解

\int_{4}^{7} (x - 5)^{2} d x

3

解答ステップ

\int_{4}^{7} (x - 5)^{2} d x

拡張

(x - 5)^{2} : x^{2} - 10 x + 25

= \int_{4}^{7} x^{2} - 10 x + 25 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}^{7} x^{2} d x - \int_{4}^{7} 10 x d x + \int_{4}^{7} 25 d x

\int_{4}^{7} x^{2} d x = 93

\int_{4}^{7} 10 x d x = 165

\int_{4}^{7} 25 d x = 75

= 93 - 165 + 75

簡素化

= 3