- #1

rodneyspencer

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## Homework Statement

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

## Homework Equations

Washer method (about x):

V = pi [tex]\int^b_a[/tex] ((R

_{top}

^{2}(x) - r

_{bottom}

^{2}(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.

Washer:

V = pi [tex]\int^8_0[/tex] ((x/4)

^{2})dx = 32pi/3

Shell:

V = 2pi [tex]\int^2_0[/tex] (y(4y))dy = 64pi/3

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