integral from 0 to 4 of-6x^2-12x+144

解

\int_{0}^{4} - 6 x^{2} - 12 x + 144 d x

352

解答ステップ

\int_{0}^{4} - 6 x^{2} - 12 x + 144 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}^{4} 6 x^{2} d x - \int_{0}^{4} 12 x d x + \int_{0}^{4} 144 d x

\int_{0}^{4} 6 x^{2} d x = 128

\int_{0}^{4} 12 x d x = 96

\int_{0}^{4} 144 d x = 576

= - 128 - 96 + 576

簡素化

= 352