integral from 2 to 6 of (6x+2)^2

解

\int_{2}^{6} (6 x + 2)^{2} d x

2896

解答ステップ

\int_{2}^{6} (6 x + 2)^{2} d x

拡張

(6 x + 2)^{2} : 36 x^{2} + 24 x + 4

= \int_{2}^{6} 36 x^{2} + 24 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}^{6} 36 x^{2} d x + \int_{2}^{6} 24 x d x + \int_{2}^{6} 4 d x

\int_{2}^{6} 36 x^{2} d x = 2496

\int_{2}^{6} 24 x d x = 384

\int_{2}^{6} 4 d x = 16

= 2496 + 384 + 16

簡素化

= 2896