integral from 0 to 2 of (x^2-9x+14)

解

\int_{0}^{2} (x^{2} - 9 x + 14) d x

\frac{38}{3}

十進法表記

12.66666 \dots

解答ステップ

\int_{0}^{2} x^{2} - 9 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} 9 x d x + \int_{0}^{2} 14 d x

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

\int_{0}^{2} 9 x d x = 18

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

= \frac{8}{3} - 18 + 28

簡素化

\frac{8}{3} - 18 + 28 : \frac{38}{3}

= \frac{38}{3}