integral from-2 to 1 of (x-2)^2

解

\int_{- 2}^{1} (x - 2)^{2} d x

21

解答ステップ

\int_{- 2}^{1} (x - 2)^{2} d x

拡張

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

= \int_{- 2}^{1} x^{2} - 4 x + 4 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}^{1} x^{2} d x - \int_{- 2}^{1} 4 x d x + \int_{- 2}^{1} 4 d x

\int_{- 2}^{1} x^{2} d x = 3

\int_{- 2}^{1} 4 x d x = - 6

\int_{- 2}^{1} 4 d x = 12

= 3 - (- 6) + 12

簡素化

= 21