integral from 2 to 3 of x^2+2x+2-5

解

\int_{2}^{3} x^{2} + 2 x + 2 - 5 d x

\frac{25}{3}

十進法表記

8.33333 \dots

解答ステップ

\int_{2}^{3} x^{2} + 2 x + 2 - 5 d x

簡素化

= \int_{2}^{3} x^{2} + 2 x - 3 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_{2}^{3} x^{2} d x + \int_{2}^{3} 2 x d x - \int_{2}^{3} 3 d x

\int_{2}^{3} x^{2} d x = \frac{19}{3}

\int_{2}^{3} 2 x d x = 5

\int_{2}^{3} 3 d x = 3

= \frac{19}{3} + 5 - 3

簡素化

\frac{19}{3} + 5 - 3 : \frac{25}{3}

= \frac{25}{3}