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

解

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

54

解答ステップ

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

\int_{1}^{3} 4 x^{3} d x = 80

\int_{1}^{3} 3 x^{2} d x = 26

= 80 - 26

簡素化

= 54