How to Derive the Joint PDF Using the Ratio of Uniforms Method?

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crazy2006
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Hi everybody:
I am trying to solve this question:
[URL=http://imageshugger.com/][PLAIN]http://imageshugger.com/images/wviidazp3mf06ej32.jpg[/URL]

I have made the following:
u=y
v=xy

Calculated the Jacobian, which is |-y|=y
then as I know that is unnormalized I need to normalized first using a double integral as a normalizing factor, the thing is that I am stuck there :cry:
please could you help me to get the joint pdf of X and Y
thanks
 
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no homework, this question is posted in a book about probability and also it is somewhat explained into the paper of 1977 of Kinderman and Monahan, but as I said I got stucked into the joint pdf and not get the answer
any help would be valuable