Integral conversion to polar coordinates - bounds $\int\limits_0^1 \int\limits_0^1\sqrt{x^2+y^2}\ dxdy$ I have an integral
$$\int_0^1 \int_0^1\sqrt{x^2+y^2}\ dxdy $$
and its result is $\approx0.765...$
I convert it to polar coordinates and get
$$\int_a^b \int_c^dr\ drd\phi $$
But how can I compute $a,b,c,d$?

I do not believe that polar coordinates are the best approach, since they are not suitable for describing a square. Anyway, if you fix an angle $0 \leq \phi < 2\pi$, you must compute the length of the segment that joins the origin with the boundary of the square and with angular coefficient $\tan \phi$. This length depends on $\phi$, but I am unsure if the iterated integral becomes easy.
