integral from-2 to 3 of x^2-x-6

解答

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

- \frac{125}{6}

十进制

- 20.83333 \dots

求解步骤

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

使用积分加法定则:

\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

化简

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

= - \frac{125}{6}