When I have a problem such as

if f(x,y) = 2e^(-x-2y) , x>0, y>0 and 0 elsewhere find the integral when x< 2y

after drawing the picture, it seems like I could either first integrate over x x from 0 to 2 and then over y from x/2 to x or reverse. But only this one gives the right answer. What am I getting the answer to when I switch it?