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

解

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

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

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

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

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

簡素化

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

= \frac{125}{6}