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

解

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

- \frac{125}{6}

十進法表記

- 20.83333 \dots

解答ステップ

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

拡張

(x + 2) (x - 3) : x^{2} - x - 6

= \int_{- 2}^{3} x^{2} - 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_{- 2}^{3} x^{2} d x - \int_{- 2}^{3} x d x - \int_{- 2}^{3} 6 d x

\int_{- 2}^{3} x^{2} d x = \frac{35}{3}

\int_{- 2}^{3} x d x = \frac{5}{2}

\int_{- 2}^{3} 6 d x = 30

= \frac{35}{3} - \frac{5}{2} - 30

簡素化

\frac{35}{3} - \frac{5}{2} - 30 : - \frac{125}{6}

= - \frac{125}{6}