integral from 1 to 2 of (4x^3-3x^2+2x)

解

\int_{1}^{2} (4 x^{3} - 3 x^{2} + 2 x) d x

11

解答ステップ

\int_{1}^{2} 4 x^{3} - 3 x^{2} + 2 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_{1}^{2} 4 x^{3} d x - \int_{1}^{2} 3 x^{2} d x + \int_{1}^{2} 2 x d x

\int_{1}^{2} 4 x^{3} d x = 15

\int_{1}^{2} 3 x^{2} d x = 7

\int_{1}^{2} 2 x d x = 3

= 15 - 7 + 3

簡素化

= 11