I have a question regarding problem solving tips. When given an iterated integral and asked to convert it to polar coordinates, how do you select the bounds of theta - do you have to understand how the graph of r operates and therefore know where the theta bounds are based on the rectangular coordinate bounds (aka completely conceptual)? Or is there a mathematical way of solving for the theta bounds? For instance: Set up a double integral in polar coordinates for: f(x,y) = x+y R: x^2 + y^2 ≤ 4 x ≥ 0 y ≥ 0 Obviously, the theta bounds are from 0->pi/2 because of the y and x bounds, but is there a mathematical procedure to arrive at this same answer? Or must you figure it out conceptually. Thank you in advance for your help!