1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Dick

    User Avatar
    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook