[quote][b]Posted by:[/b] Disambiguation [quote][b]Posted by:[/b] prometheus25 Read over the document I linked. Orthogonality of x and y is an issue to me. Also, the polar integration can be done equivalently by [url=http://www.wolframalpha.com/input/?i=integral+%28integral+re^%28-r^2%29+theta+%3D+0+to+pi%29+r+%3D+-infinity+to+infinity]int(-a,a)int(0,pi)e^(-x^2)rdthetadr[/url], which gives you an answer of 0.[/quote]Orthogonality of x and y has nothing to do with the polar transformation; and you're still erroneously integrating r from -inf to inf, which doesn't even make sense. r is a nonnegative quantity.[/quote] You can absolutely have a negative radius. It's not mathematically incorrect. In that case, I am integrating a positive infinite radius in one direction by 180 degrees (pi radians) while simultaneousness integrating a negative radius in the exact opposite direction 180 degrees (pi radians). It's the equivalent of a two-bladed propeller (with blades of infinite length, of course) spinning 180 degrees, but each one, being mounted exactly opposite each other, cover half the area of a full circle. Mathematically this is equal to a single "blade" being spun a full 360 degrees. Edit: Further more, orthogonality has [i]everything[/i] to do with polar integration. The reason that you can substitute x^2 + y^2 for r^2 is because they are right angles to each other, allowing for the Pythagorean Theorem to be employed to find the length of the hypotenuse, which is the radius. It also means that they are out of phase. I assure you this is mathematically correct. I am a 4th year Electrical Engineer, too, ya know. That puts my credentials exactly where you are. [Edited on 02.14.2012 7:05 PM PST]