derived probability density function

I have a problem about derive a pdf from two marginal pdfs:

random variables x and y are distributed according to the joint probability density function (pdf):

fxy(x,y) = 3x/2 , if 1 <= x <= y <= 2

0 , otherwhise

Random variable z is defined by z = y - x

Determine the probablity density function fz(z)

thanks.

can you complete the integral?

can you finish the integral?

of the problem to obtain the derived pdf?

what about the integral related to "y"?

I've noticed that you integrated respect to "x", but as far as I know, if you want to derive a pdf from two random variables, the limits must be according to the marginal "x" and "y" pdfs.