I am in the middle of an exercice dealing with this joint density function :
$$ f_{x,y}(x,y) = \frac{x^2+y}{a}$$ for $ 0 < x < y < 2$
I have been asked to compute the marginal densities and I know how to do it but I am struggling with the bounds. To verify that this joint density function is legit, I found the value of a using this boundaries :
$$ \int_{0}^{2}\int_{x}^{2} \frac{x^2+y}{a} \,dydx $$
This bounds makes perfect sense and I found $a = 4$
My problem is when it comes to the marginal
I started like this using the same bounds for x : $$ \int_{x}^{2} \frac{x^2+y}{4} \,dy$$
Then, I was about to do this :
$$ \int_{0}^{2} \frac{x^2+y}{4} \,dx$$
But the solutions say that we have to do it on the interval from 0 to y.
Could you explain me why ?