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

解

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

\frac{9}{2}

十進法表記

4.5

解答ステップ

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

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

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

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

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

簡素化

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

= \frac{9}{2}