I'm looking for some guiddance on how to find the limits of integration when changing from cartesian coordinates to polar coordinates, I don't seem to be able to get correctly the interval where $r$ takes values. For example in this problem:
Express the double integral $\iint_sf(x,y)dxdy$ as an iterated integral in polar coordinates:
$S=\{(x,y)|x^2<y<1, -1<x<1\}$
So the region $S$ would be the part under the line $y=1$ and over $y=x^2$, but I don't know how to find the values of $r$ and $\theta$ in the $r\theta$ plane. Any help would be appreciate it.
Also if you could give any tips to find the limits of integration in an arbitrary case it would be of so much help.
Thanks.