integral from 0 to 2 of ((-x+5)-(x^2-9))

解

\int_{0}^{2} ((- x + 5) - (x^{2} - 9)) d x

\frac{70}{3}

十進法表記

23.33333 \dots

解答ステップ

\int_{0}^{2} - x + 5 - (x^{2} - 9) d x

簡素化

= \int_{0}^{2} - x^{2} - x + 14 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^{2} d x - \int_{0}^{2} x d x + \int_{0}^{2} 14 d x

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

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

\int_{0}^{2} 14 d x = 28

= - \frac{8}{3} - 2 + 28

簡素化

- \frac{8}{3} - 2 + 28 : \frac{70}{3}

= \frac{70}{3}