Okay, so I have a calc exam this Friday. He said he wont be asked to prove that double integral of f(x,y) is equal to rcos(t)*rsin(t)*r*dr*dt in polar coordinates, but that it's fair game to ask some theoretical question about it. We didn't go into a lot of detail about this in class. I believe he will ask about the additional "r" that is tagged to the end; there's nothing else he can really ask about it in my opinion. Why does this "r" exist?