# Improper integrals and canceling of areas

1. Mar 31, 2013

### nick.martinez

When evaluating an improper integral and i get infinity minus infitiy when taking the limit. in what case do the areas cancel?

2. Mar 31, 2013

### SteamKing

Staff Emeritus
Infinity minus infinity is not equal to zero. You have a divergent integral.

3. Mar 31, 2013

### HallsofIvy

Staff Emeritus
In general, no. If f has, for example, a singularity at x= b, where a< b< c, then $$\int_a^c f(x)dx= \lim_{\alpha\to b}\int_a^\alpha f(x)dx+ \lim_{\beta\to b}\int_\beta^c f(x)dx$$.

Those two limits have to be taken independently so you cannot cancel them.