# Thread: Multiple Integration over non-Elementary Regions

1. ## Multiple Integration over non-Elementary Regions

So in my multivariable calculus text they explain a process of integrating over a region which was defined as the area between a circle of radius 2 and a circle of radius 1 both centered on (0,0). The text goes through a tedious process of breaking the region into 4 parts and adding them together. Would it be possible to integrate over the larger circle and then subtract the integral under the small circle?

2. Originally Posted by jameselmore91
So in my multivariable calculus text they explain a process of integrating over a region which was defined as the area between a circle of radius 2 and a circle of radius 1 both centered on (0,0). The text goes through a tedious process of breaking the region into 4 parts and adding them together. Would it be possible to integrate over the larger circle and then subtract the integral under the small circle?
That method would work well provided that the function was integrable over the disc of radius 2. But it would break down for a function such as $\displaystyle 1/(x^2+y^2)$, where the integral over the larger disc and the integral over the small disc are both infinite.

3. Thanks, that was my assumption.