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Finite area with infinite volume

  1. Oct 30, 2004 #1
    I know that f(x)= 1/x has a infinite area from 1 to infinity but if this area is roated about the x-axis it gives a finite volume. It's actually Torricelli's trumpet.

    However, I can't think of any infinite region with a finite area that when rotated about the y-axis gives an infinite volume.

    Any help is welcome.

  2. jcsd
  3. Oct 30, 2004 #2


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    In light of that, have you thought about trying to prove that rotating a finite area around the y-axis always yields a finite volume?
  4. Nov 2, 2004 #3
    How would you suggest that I try proving that an infinite region which holds a finite area, always gives a finite volume when rotated around the y-axis.

    To be honest it is a question on my assignment, so I'm thinking there has to be an answer for it.

    Any hints are accepted
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