integral from 0 to 6 of (8x-1)^2

解

\int_{0}^{6} (8 x - 1)^{2} d x

4326

解答ステップ

\int_{0}^{6} (8 x - 1)^{2} d x

拡張

(8 x - 1)^{2} : 64 x^{2} - 16 x + 1

= \int_{0}^{6} 64 x^{2} - 16 x + 1 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}^{6} 64 x^{2} d x - \int_{0}^{6} 16 x d x + \int_{0}^{6} 1 d x

\int_{0}^{6} 64 x^{2} d x = 4608

\int_{0}^{6} 16 x d x = 288

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

= 4608 - 288 + 6

簡素化

= 4326