integral from 0 to 2 of (x+2-x^2)

解

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

\frac{10}{3}

十進法表記

3.33333 \dots

解答ステップ

\int_{0}^{2} x + 2 - 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}^{2} x d x + \int_{0}^{2} 2 d x - \int_{0}^{2} x^{2} d x

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

\int_{0}^{2} 2 d x = 4

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

= 2 + 4 - \frac{8}{3}

簡素化

2 + 4 - \frac{8}{3} : \frac{10}{3}

= \frac{10}{3}