Find the volume generated by rotating the given region about the given line using the Shell method and the Washer method.
x = 4y [y = x/4], y = 0, x = 0, x = 8 about x
Washer method (about x):
V = pi [tex]\int^b_a[/tex] ((Rtop2(x) - rbottom2(x))dx
Shell method (about x):
V = 2pi [tex]\int^d_c[/tex] (y[f(y)-g(y)])dy
The Attempt at a Solution
I'm not sure why I can't reconcile these two answers. I'm having some similar problems with more of these exercises but if someone can help me see where I'm going wrong I'm sure I can rework them successfully.
V = pi [tex]\int^8_0[/tex] ((x/4)2)dx = 32pi/3
V = 2pi [tex]\int^2_0[/tex] (y(4y))dy = 64pi/3