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Triple Integrals: Finding Mass of a Bounded Solid

  1. Jun 7, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the mass of a solid of constant density that is bounded by the parabolic cylinder x=y2 and the planes x=z, z=0, and x=1.

    3. The attempt at a solution
    https://dl.dropbox.com/u/64325990/Photobook/Photo%202012-06-07%202%2033%2024%20PM.jpg [Broken]

    I first drew some diagrams to help me visualize the problem and then I tried to solve this integral but it ended up to be in terms of x. What am I doing wrong?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jun 7, 2012 #2
    If you want to integrate in the order x, then y then z, then...

    For an arbitrary (y,z), x should go from the z=x plane to the x=1 plane,
    that is, x=z..1.

    For an arbitrary z, y should go from -√x to √x.

    Then z should go from 0 to 1.

    So your last limit should not be a function of x, nor y.


    You may want to draw all surfaces in one 3d pic. so you can see that the lower limit in x should have been x=z, not x=y^2.
    You may want to consider othe orders of integration, so that you avoid the square roots.
     
  4. Jun 7, 2012 #3

    SammyS

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    If you integrate w.r.t. x first (inner integral)n then there shouldn't any x in the limits of the outer two integrals.
     
    Last edited by a moderator: May 6, 2017
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