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

解答

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

发散

求解步骤

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

找到无定义的点（奇点）:

x = 0

如果存在

b, a < b < c, f (b) =

无定义

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

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

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

发散

如果表达式有部分发散，则整个表达式发散

= 发散

\int_{0}^{e} (\frac{x ^{2} - 9}{x + 3}) d x

\int_{- 1}^{4} 2 d x

\int_{1}^{7} t^{2} - 2 t - 24 d t

\int_{0}^{1} 3 x^{2} e^{x^{3}} d x

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