Hi,
I'm having a few issues getting this one sorted. Take a look and see if you can pick where I went wrong with it.
Thanks
Splint
Here moment of inertia about $\displaystyle x$ axis is:
$\displaystyle I_x = \int_0^2 \int_{0}^{\sqrt[3]{2x^2}} y^2\, \delta(x,y)\,\, dy\,\, dx$
If density is uniform $\displaystyle \delta(x,y) = 1$
Now you can do the rest.