integral from-1 to 1 of (x^3-2x^2-5x+6)

解

\int_{- 1}^{1} (x^{3} - 2 x^{2} - 5 x + 6) d x

\frac{32}{3}

十進法表記

10.66666 \dots

解答ステップ

\int_{- 1}^{1} x^{3} - 2 x^{2} - 5 x + 6 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_{- 1}^{1} x^{3} d x - \int_{- 1}^{1} 2 x^{2} d x - \int_{- 1}^{1} 5 x d x + \int_{- 1}^{1} 6 d x

\int_{- 1}^{1} x^{3} d x = 0

\int_{- 1}^{1} 2 x^{2} d x = \frac{4}{3}

\int_{- 1}^{1} 5 x d x = 0

\int_{- 1}^{1} 6 d x = 12

= 0 - \frac{4}{3} - 0 + 12

簡素化

0 - \frac{4}{3} - 0 + 12 : \frac{32}{3}

= \frac{32}{3}