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

解

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

\frac{25}{3}

十進法表記

8.33333 \dots

解答ステップ

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

\int_{0}^{5} 4 x d x = 50

\int_{0}^{5} x^{2} d x = \frac{125}{3}

= 50 - \frac{125}{3}

簡素化

50 - \frac{125}{3} : \frac{25}{3}

= \frac{25}{3}