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Method of shells around a different axis

  • Thread starter Jbreezy
  • Start date
  • #1
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Homework Statement



Use the method of cylindrical shells to find the volume generated by rotation the region bounded by the given curves about the specified axis.

Homework Equations




y = x^2, y = 2-x^2; about x = 1

The Attempt at a Solution



I tried to just break it down.
I want something of the form 2∏rhΔr
OK so To find the height f(x) I subtracted.
2-x^2-x^2 = 2-2x^2. For the radius I did a-x so 1-x is the radius


So I have

V = 2∏∫ (1-x)(2-2x^2)dx between -1 and 1 because that is where the graphs intersect.
Evaluating it I got 2∏((x^4)/2 -(2x^3)/3 -x^2 +2x ] between -1 and 1

I got 16∏/3
Is this the right way?
 

Answers and Replies

  • #2
CAF123
Gold Member
2,895
88
Yes, it is correct. Try doing it using disks and see if you can obtain the same answer. This will allow you to compare the complexity of the resulting integrals and see why one method is more efficient than the other in this case.
 

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