integral from 0 to 10 of-6x^2-12x+720

解

\int_{0}^{10} - 6 x^{2} - 12 x + 720 d x

4600

解答ステップ

\int_{0}^{10} - 6 x^{2} - 12 x + 720 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}^{10} 6 x^{2} d x - \int_{0}^{10} 12 x d x + \int_{0}^{10} 720 d x

\int_{0}^{10} 6 x^{2} d x = 2000

\int_{0}^{10} 12 x d x = 600

\int_{0}^{10} 720 d x = 7200

= - 2000 - 600 + 7200

簡素化

= 4600