Volume of revolution about the line $y = 2$ of region bounded by $x=y^3$ and $y=x^2$ I need to find the volume of the solid generated by revolving the region bounded by the graphs of the equations $x=y^3$ and $y=x^2$ about the line $y=2$.
My Attempt: $\pi \int_0^1 (2-x^2)^2-(2-x^{1/3})^2 dx$
Is this set up correct? 

Yes you are correct in your derivation.
A graphical representation of your answer:

