integral from 0 to 2 of 4x^2-2x^3

解

\int_{0}^{2} 4 x^{2} - 2 x^{3} d x

\frac{8}{3}

十進法表記

2.66666 \dots

解答ステップ

\int_{0}^{2} 4 x^{2} - 2 x^{3} 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}^{2} 4 x^{2} d x - \int_{0}^{2} 2 x^{3} d x

\int_{0}^{2} 4 x^{2} d x = \frac{32}{3}

\int_{0}^{2} 2 x^{3} d x = 8

= \frac{32}{3} - 8

簡素化

\frac{32}{3} - 8 : \frac{8}{3}

= \frac{8}{3}