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

解

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

\frac{10}{3}

十進法表記

3.33333 \dots

解答ステップ

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

簡素化

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

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

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

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

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

簡素化

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

= \frac{10}{3}