integral from-2 to 1 of (4-x^2)-(x+2)

解

\int_{- 2}^{1} (4 - x^{2}) - (x + 2) d x

\frac{9}{2}

十進法表記

4.5

解答ステップ

\int_{- 2}^{1} 4 - x^{2} - (x + 2) d x

簡素化

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

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

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

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

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

簡素化

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

= \frac{9}{2}