integral from 0 to 1 of (3x-2)^2

解

\int_{0}^{1} (3 x - 2)^{2} d x

1

解答ステップ

\int_{0}^{1} (3 x - 2)^{2} d x

拡張

(3 x - 2)^{2} : 9 x^{2} - 12 x + 4

= \int_{0}^{1} 9 x^{2} - 12 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_{0}^{1} 9 x^{2} d x - \int_{0}^{1} 12 x d x + \int_{0}^{1} 4 d x

\int_{0}^{1} 9 x^{2} d x = 3

\int_{0}^{1} 12 x d x = 6

\int_{0}^{1} 4 d x = 4

= 3 - 6 + 4

簡素化

= 1