integral from 0 to 6 of (x+2)^2

解

\int_{0}^{6} (x + 2)^{2} d x

168

解答ステップ

\int_{0}^{6} (x + 2)^{2} d x

拡張

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

= \int_{0}^{6} 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_{0}^{6} x^{2} d x + \int_{0}^{6} 4 x d x + \int_{0}^{6} 4 d x

\int_{0}^{6} x^{2} d x = 72

\int_{0}^{6} 4 x d x = 72

\int_{0}^{6} 4 d x = 24

= 72 + 72 + 24

簡素化

= 168