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Volume by Shell and Washer Methods

  • #1

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] ((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.

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
 

Attachments

Last edited:

Answers and Replies

  • #2
I forgot about x=8. The shell method should be V = 2pi [tex]\int^2_0[/tex] (y(8-(4y)))dy = 32pi/3.

:facepalm:
 
  • #3
Double-post :/

:facepalm:
 
Last edited:

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