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

解

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

\frac{32}{3}

十進法表記

10.66666 \dots

解答ステップ

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

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

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

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

= 12 + 8 - \frac{28}{3}

簡素化

12 + 8 - \frac{28}{3} : \frac{32}{3}

= \frac{32}{3}