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

解

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

\frac{32}{3}

十進法表記

10.66666 \dots

解答ステップ

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

簡素化

= \int_{- 2}^{2} - x^{2} + 4 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}^{2} x^{2} d x + \int_{- 2}^{2} 4 d x

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

\int_{- 2}^{2} 4 d x = 16

= - \frac{16}{3} + 16

簡素化

- \frac{16}{3} + 16 : \frac{32}{3}

= \frac{32}{3}