Improper integrals and canceling of areas

[nick.martinez]

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

 

[SteamKing]

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

 

[HallsofIvy]

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.