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

解

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

\frac{32}{3}

十進法表記

10.66666 \dots

解答ステップ

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

\int_{- 3}^{1} 3 d x = 12

\int_{- 3}^{1} x^{2} d x = \frac{28}{3}

\int_{- 3}^{1} 2 x d x = - 8

= 12 - \frac{28}{3} - (- 8)

簡素化

12 - \frac{28}{3} - (- 8) : \frac{32}{3}

= \frac{32}{3}