integral from-1 to 2 of [(x+3)-(x^2+1)]

解

\int_{- 1}^{2} [(x + 3) - (x^{2} + 1)] d x

\frac{9}{2}

十進法表記

4.5

解答ステップ

\int_{- 1}^{2} x + 3 - (x^{2} + 1) d x

簡素化

= \int_{- 1}^{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_{- 1}^{2} x^{2} d x + \int_{- 1}^{2} x d x + \int_{- 1}^{2} 2 d x

\int_{- 1}^{2} x^{2} d x = 3

\int_{- 1}^{2} x d x = \frac{3}{2}

\int_{- 1}^{2} 2 d x = 6

= - 3 + \frac{3}{2} + 6

簡素化

- 3 + \frac{3}{2} + 6 : \frac{9}{2}

= \frac{9}{2}