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Volume Integral Problem

  1. Dec 5, 2004 #1
    I'm have trouble trying to evaluate the volume integral (shown in question.gif).

    I've attempted integrating it a few different ways, either achieveing an answer of 3 or 5.75, and i'm not sure where i'm going wrong. (Some of what i've done is in attempted_solution.gif)

    Any comments gratefully received....
     

    Attached Files:

  2. jcsd
  3. Dec 5, 2004 #2

    arildno

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    Dearly Missed

    Your upper limits are not meaningful!
    Let's look at this closely:
    a) 0<=y<=3
    These bounds should be obvious.
    b) 0<=x and 0<=z
    Okay?
    c) Now, to the last limit indicated by the plane x+z=1
    Since, by b) neither x or z can be negative, we can choose the following limits:
    0<=x<=1
    0<=z<=1-x

    Okay with this?
     
  4. Dec 5, 2004 #3

    dextercioby

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    Since we're speaking about the triorthogonal tetrahedron determined by the intersection of the plane [itex] 3x+y+3z=3 [/itex] with the coordinate axes,maybe a graphical representation might help.
    Chosing the integration limits correctly (the way Arildno showed you),u find after easy calculations that the integral should yield 1.
     
  5. Dec 5, 2004 #4
    Yes, i've got it now. Thanks.

    :rofl:
     
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