Hey, I am doing a homework exercise and I think im getting the wrong answer. I have to work out a marginal distribution from a joint distribution. So I use the definition of marginal distribution for the continous case.

$\displaystyle f_y(y)=\int_{X}f_{X,Y}(x,y) dx$. When I evalute my integral it gives me infinite, could this be right? Are the other ways to do it? At first the problem gave me to random variables X and Y, with density functions $\displaystyle \frac{-x^2}{75}-\frac{6x}{75} + \frac{8}{15}$ when 0<=x<=3 and Y distributed uniformly between half of X and two times X. To find the joint distribution I used the following formula

Where $\displaystyle f_{Y|X}(y|x)= Y$ when x is choosen and $\displaystyle f_{X}(x)= X$.

The integral im evaluating to get the marginal distribution is

Your help is greatly apreciated.