integral from 2 to 4 of (x^3-6x^2+8x)

解

\int_{2}^{4} (x^{3} - 6 x^{2} + 8 x) d x

- 4

解答ステップ

\int_{2}^{4} x^{3} - 6 x^{2} + 8 x 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}^{4} x^{3} d x - \int_{2}^{4} 6 x^{2} d x + \int_{2}^{4} 8 x d x

\int_{2}^{4} x^{3} d x = 60

\int_{2}^{4} 6 x^{2} d x = 112

\int_{2}^{4} 8 x d x = 48

= 60 - 112 + 48

簡素化

= - 4