Does anybody know how to get the surface area under this parametric curve about the x axis? I've been trying for hours..

x= 8(t^2)

y= 64t - (t^3)/3

0 <= t <= 8sqrt(3)

My work:

S = 2pi(integral(((64t - (t^3)/3)sqrt((16t^2 + (64-t^2)^2)dt

from 0 to 8sqrt(3)

S = 2pi(integral(((64t - (t^3)/3)sqrt((128t^2+4096t^4)dt

from 0 to 8sqrt(3)