integral from-2 to 3 of x^{-3}

解答

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

发散

求解步骤

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

\int_{- 2}^{0} x^{- 3} 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}^{1} 15 e^{3 x} d x

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

\int_{1}^{4} (t + \frac{1}{t})^{2} d t

\int_{0}^{4} x \cdot \frac{x}{8} d x

\int_{1}^{4} (4 x^{2} - 9 x) d x