integral from 0 to 4 of 1/((x-2)^2)

解答

\int_{0}^{4} \frac{1}{( x - 2 ) ^{2}} d x

发散

求解步骤

\int_{0}^{4} \frac{1}{( x - 2 ) ^{2}} d x

找到无定义的点（奇点）:

x = 2

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_{0}^{2} \frac{1}{( x - 2 ) ^{2}} d x + \int_{2}^{4} \frac{1}{( x - 2 ) ^{2}} d x

\int_{0}^{2} \frac{1}{( x - 2 ) ^{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}^{a} sin (\frac{π x}{a}) d x

\int_{0}^{1} (y^{4} + y^{6}) d y

\int_{\frac{π}{6}}^{\frac{π}{3}} cos (3 x) d x

\int_{- 2 π}^{2 π} 5 sin (x) d x

\int_{0}^{0.5} sin (π t) d t