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

解答

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

- \frac{46}{3}

十进制

- 15.33333 \dots

求解步骤

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

\int_{- 1}^{3} \frac{1}{2} x^{2} d x = \frac{14}{3}

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

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

= \frac{14}{3} - 8 - 12

化简

\frac{14}{3} - 8 - 12 : - \frac{46}{3}

= - \frac{46}{3}