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

解

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

\frac{40}{3}

十進法表記

13.33333 \dots

解答ステップ

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

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

\int_{- 2}^{2} 2 x d x = 0

\int_{- 2}^{2} 2 d x = 8

= \frac{16}{3} - 0 + 8

簡素化

\frac{16}{3} - 0 + 8 : \frac{40}{3}

= \frac{40}{3}