# Math Help - Integrating within a circle?

1. ## Integrating within a circle?

Integrate $\frac{\ln\left({x^{2}+y^{2}}\right)}{x^{2}+y^{2}}$ over the region between the circles $x^{2}+y^{2}=1$ and $x^{2}+y^{2}=e^{2}$.

So the integration itself is fine using the quotient rule, but how do I use the circles to get the limits of integration?

2. This problem works great in polar coordinates, but I think you made a typo because as written the numerator and denominator are the same.

EDIT: I see you already noticed this.

Ok, so in polar coordinates $r^2=x^2+y^2$ and the area of $A(r(\theta))=\frac{1}{2} \int r^2d\theta$. So now you need to express the region in terms of polar coordinates, which should be easy since $r(\theta)=a$ is a circle with radius a.