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Determining Volume using double integral

  1. Feb 9, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid in the first octant by the planes z = x + y + 1 and z = 5 - x - y

    2. Relevant equations



    3. The attempt at a solution

    How would I set this up?
     
  2. jcsd
  3. Feb 9, 2009 #2

    Dick

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    You would set it up by drawing the region in the z=0 (i.e. xy plane) and integrating z*dx*dy over that region.
     
  4. Feb 11, 2009 #3
    Are you sure it's not supposed to be dz dy dx? I went to my prof with this one, and the way he set it up as a series of triple integrals.
     
  5. Feb 11, 2009 #4

    Dick

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    Your post title was "Determining Volume using double integral". It you want to set it up as a triple integral first then you integrate 1*dz*dx*dy over the volume. The integral of 1*dz is just z. It's the same thing. Now get started.
     
  6. Feb 11, 2009 #5
    http://img16.imageshack.us/img16/1340/39161133fw1.jpg [Broken]

    Its not to scale though; I just need to worry about the top right quadrant.

    [tex]\int^{5}_{0}\int^{x - 5}_{0}\int^{5- x - y}_{0} dz dy dx + \int^{1}_{0}\int^{-x - 1}_{0}\int^{x + y +1}_{0} dz dy dx[/tex]

    How off am I?
     
    Last edited by a moderator: May 4, 2017
  7. Feb 11, 2009 #6

    Dick

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    Not too good I don't think. I'm not too sure what you are trying to draw, but your first step should be to figure out where the two planes intersect. Can you do that? I think that will help you picture the region.
     
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