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Another Triple Integral Question

  1. Apr 10, 2004 #1

    Here is the original question http://phasedma.com/uploaded/TripleIntegral.JPG

    My difficuly is understanding the limits of integration--- party due to how the solid in question is "sliced" by those planes. I know how to visualize the parabolic cylinder, but I need help on 1. limits on integration, and 2. Order of integration.

    I doubt I would have to use polar coordinates since the region in question has no square roots...

    Thanks for you help I really do appreciate this.
  2. jcsd
  3. Apr 10, 2004 #2
    Arghh that links not working, just copy paste it into the url. Sorry.
  4. Apr 10, 2004 #3
    TEChild, you can use Latex coding here, click on this link:

    [tex]\int \int \int_E (x + 2y)dV[/tex]

    where E is bound by the parabolic cylinder


    and the planes

    Last edited: Apr 10, 2004
  5. Apr 10, 2004 #4
    Divide and conquer. z appears as an independent variable once and as a constant. So, easy to eliminate x:

    [tex]\int _E ()dV = \int_0^1 dz \int dy \int_z^1 ()dx[/tex]

    Do you see why the upper limit on z is 1? Solve the innermost integral as tho y and z were constants.
  6. Apr 10, 2004 #5
    actually I dont see why the upper limit on z is one... thats where I was confused --- I understand why it starts at 0 of course... and also the y limits are giving me trouble...
  7. Apr 11, 2004 #6
    taking z as the independent variable, ask yourself: what is the greatest z value a point in the bounded volume can have?
  8. Apr 11, 2004 #7
    ahhhh i got it thanks so much
  9. Apr 11, 2004 #8
    Ooh Bellingham--- are you a graduate student at Western Washington U. outandbeyond?
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