integral from-2 to 1 of 2-x-x^2

解

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

\frac{9}{2}

十進法表記

4.5

解答ステップ

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

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

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

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

= 6 - (- \frac{3}{2}) - 3

簡素化

6 - (- \frac{3}{2}) - 3 : \frac{9}{2}

= \frac{9}{2}