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Triple integral forming a solid region

  1. Sep 15, 2016 #1
    1. The problem statement, all variables and given/known data
    upload_2016-9-14_21-8-49.png

    2. Relevant equations
    Fubini's theorum

    3. The attempt at a solution
    I drawn the diagram with the limits (for x, y, and z)
    and come up with something with 4 faces, 5 corners, 8 edges

    is that something you guys got? Thanks
     
  2. jcsd
  3. Sep 15, 2016 #2

    andrewkirk

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    The number of corners and edges are correct. I don't think the number of faces is.
     
  4. Sep 15, 2016 #3

    BvU

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    I also come up with a different number of faces
     
  5. Sep 15, 2016 #4
    Like how many as what am I doing wrong??

    upload_2016-9-15_8-50-27.png


    The x limit is 0 and z, so for z, it is between y and 1, so I put 1 as upper limit for x.
     
  6. Sep 15, 2016 #5
    upload_2016-9-15_8-53-51.png
     
  7. Sep 15, 2016 #6

    LCKurtz

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    One of the faces is part of the plane ##x=z##. You don't have that in your picture.
     
  8. Sep 15, 2016 #7

    BvU

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    I count five faces on your drawings too...
    z = 1 is one plane, a square face
    x = 0 is a triangular face
    y = 0 is a triangular face, not a square face: x runs from 0 to z, not from 0 to 1.
    the other two triangular faces have x=y=z as edge in common
     
  9. Sep 15, 2016 #8
    so it's like a square on top with the edges pointering to a single point on bottom?
     
  10. Sep 15, 2016 #9

    andrewkirk

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    That's right - like the Great Pyramid (disregarding the references to 'top' and 'bottom'). This shape is known as a 'square pyramid'. The word 'square' is included to distinguish it from a tetrahedron or triangular pyramid. But in common language, the word 'pyramid' usually implies a square base.
     
  11. Sep 15, 2016 #10

    LCKurtz

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    Now that you have it, here's a nice picture:
    upload_2016-9-15_16-38-50.png
    Now the trick for you is to set up the six integrals. Do you see why when you do ##dz## first something is a bit more complicated?
     
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