Bounds on integration. Have answer, need clarification.
Evaluate the iterated integral by converting to polar coordinates.
I know how to do the integration part; that's not my question. My question is how the original solver of the problem came up with the bounds of integration: the first integral from 0 to pi/4 and the second from 0 to sqrt(2).
I came up with the right answer, but I think I get it using the wrong methods. I took x=sqrt(2-y^2), turned that into x^2+y^2 = 2, giving me a radius of sqrt(2), and therefore 0 <= r <= sqrt(2). For the theta however, I'm a little lost. Is it obtained simply by observing the fact that x=y makes a 45 degree angle with both axes?
Any help is greatly appreciated.