Question

Could someone please have a look at my workings (attached) and let me know if I am on the right track?

Answer 1

Don't know much about joint density functions... but the integration seems right to me.

there is just a typo in the 3rd last step; it should look more like:
\[\LARGE \left[ \ln \left( y \right) \over x\right]_{y=1}^{y=x}\]

you have already evaluated the integral to get ln(y)