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**Mysc** 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?

So if I first integrated from 0 to 2 over x that would give me the probability function for y, and then if I integrated that from y= x/2 to x does that make any kind of sense? I know it doesn't, but I don't know exactly why.