Double checking volume

[Jbreezy]

Homework Statement

Consider the region between the functions f(x) = x^2 and g(x) = 2x in the first quadrant.
Use the method of cylindrical shells to find the volume generated by rotating about the y axis.
I did this integral
V = 2∏∫x(2x-x^2) dx between [0,2]
I got 2∏((2/3)x^3 - (x^4/4) = 8∏/3

Homework Equations

I think it is OK just want someone to confirm. Before I turn in.

The Attempt at a Solution

 

[Dick]

Looks fine to me.

 

[Jbreezy]

Thanks amigo.