I've been learning about polar coordinates recently and the following problem has me stumped:
$\int_{x=0}^{x=1}\int_{y=0}^{y=1}\frac{1}{(1+x^2+y^2)^2}dydx$
I'm required to solve the above problem using polar coordinates. I do know that we could express the integrand in terms of $r$ and $\theta$ as follows:
$\frac{1}{(1+x^2+y^2)^2}dydx=\frac{1}{(1+r^2)^2}rdrd\theta$
But I'm lost as to how to proceed further. Specifically, how to convert the limits of integration in terms of $r$ and $\theta$. I'm used to using polar coordinates with circular regions only, not a rectangular (or in this case square) region. Thanks for any help.