integral from-2 to 2 of x^3-2x^2+7

解

\int_{- 2}^{2} x^{3} - 2 x^{2} + 7 d x

\frac{52}{3}

十進法表記

17.33333 \dots

解答ステップ

\int_{- 2}^{2} x^{3} - 2 x^{2} + 7 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^{3} d x - \int_{- 2}^{2} 2 x^{2} d x + \int_{- 2}^{2} 7 d x

\int_{- 2}^{2} x^{3} d x = 0

\int_{- 2}^{2} 2 x^{2} d x = \frac{32}{3}

\int_{- 2}^{2} 7 d x = 28

= 0 - \frac{32}{3} + 28

簡素化

0 - \frac{32}{3} + 28 : \frac{52}{3}

= \frac{52}{3}