Any web resources regarding changing the variable of integration from cartesian to polar coordinates that goes beyond the basic : x = r cos theta y = r sin theta r = sq rt (x^2 + y^2) I totally don't get how to find the limits of integration using polar coordinates and my undergrad textbooks appears to assume we already know it. E.g. r = 2 sin 2 theta , first quadrant. How do we find the limits of integration for r? Totally clueless. Tried googling but keep getting just the 3 definitions above. What is the general technique or algorithm?