Question

Find the volume of the solid generated when the shaded region enclosed by the graphs of f and g is revolved about the horizonal line y=2.
f(x) = 2x(1-x) and g(x) = 3(x-1)x^(1/2)

I know I'm supposed to integrate it.
V = pi * 0,integrand,1 [(2-g(x))^2 - (2-f(x))^2]dx
This is the formula, but I can't seem to get the correct answer (103/20)*pi. Please show all the steps