Integrating a function over a square using polar coordinates Say we have a function $f(x,y)$ over the unit circle. To integrate with polar coordinates we replace the x and y in $f(x,y)$ with $r\cos\theta$ and $y\sin\theta$ to get $f(r,\theta)$ and we integrate $f(r,\theta)rdrd\theta$ for $r$ between $0$ and $1$ and $\theta$ between 0 and $2\pi$. What if we want to integrate over a square using polar coordinates. What must we do?

Hint:
Write the "equation of the square" in polar coordinates.
The domain is limited on the right by the inequation $$x=\rho\cos\theta\le c$$ and this holds for $$|\theta|\le\frac\pi2.$$
You can repeat the reasoning for the four sides.
