integral from 0 to 4 of ((5x-x^2)-x)

解

\int_{0}^{4} ((5 x - x^{2}) - x) d x

\frac{32}{3}

十進法表記

10.66666 \dots

解答ステップ

\int_{0}^{4} 5 x - x^{2} - x d x

簡素化

= \int_{0}^{4} - x^{2} + 4 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_{0}^{4} x^{2} d x + \int_{0}^{4} 4 x d x

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 4 x d x = 32

= - \frac{64}{3} + 32

簡素化

- \frac{64}{3} + 32 : \frac{32}{3}

= \frac{32}{3}