integral from-2 to 0 of (x-3)(x+5)

解答

\int_{- 2}^{0} (x - 3) (x + 5) d x

- \frac{94}{3}

十进制

- 31.33333 \dots

求解步骤

\int_{- 2}^{0} (x - 3) (x + 5) d x

乘开

(x - 3) (x + 5) : x^{2} + 2 x - 15

= \int_{- 2}^{0} x^{2} + 2 x - 15 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}^{0} x^{2} d x + \int_{- 2}^{0} 2 x d x - \int_{- 2}^{0} 15 d x

\int_{- 2}^{0} x^{2} d x = \frac{8}{3}

\int_{- 2}^{0} 2 x d x = - 4

\int_{- 2}^{0} 15 d x = 30

= \frac{8}{3} - 4 - 30

化简

\frac{8}{3} - 4 - 30 : - \frac{94}{3}

= - \frac{94}{3}

\int_{0}^{k} x \cdot x^{2} + 4 d x

\int_{1}^{2} \frac{2}{x} d x

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

\int_{0}^{r} (b r^{2} + cr) (2 π r) d r

\int_{2}^{5} (3 x + x^{2} - x^{3}) d x