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Homework Help: Volumes by Slicing and Rotation about an Axis.

  1. Dec 15, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid generated by revolving the region between the parabola x = y^2 + 1 and the line x = 3 about the line x = 3.

    2. Relevant equations

    The answer is found by integrating with respect to y with disk method, but I don't understand why my answer is incorrect when I try to integrate it with dx.

    3. The attempt at a solution

    The exact answer when integrated with respect to y is 64*pi*√(2)/15.

    This is the integral I am incorrectly setting up somehow:
    2*∫ pi * (√(x-1))^2 dx, x = 1 to 3

    Any ideas why this doesn't work?
  2. jcsd
  3. Dec 15, 2012 #2


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    Science Advisor
    Homework Helper

    Integrating dy your cross sections are disks. If you want to integrate dx then your cross sections are shells. You need to use a different formula for the integral.
  4. Dec 15, 2012 #3
    The cross-section of 3-d parabola isn't a circle?... ohhh, this isn't a 3d parabola, it's rotated.

    Thank you very much!
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