integral from-2 to 3 of (x-6)-(x^2-12)

解

\int_{- 2}^{3} (x - 6) - (x^{2} - 12) d x

\frac{125}{6}

十進法表記

20.83333 \dots

解答ステップ

\int_{- 2}^{3} x - 6 - (x^{2} - 12) d x

簡素化

= \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}