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Integral with transformations and bounded by x + y + z = 1

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  1. May 18, 2017 #1

    Cyn

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    1. The problem statement, all variables and given/known data
    I have a question. I need to know the integral dxdydz/(y+z) where x>=0, y>=0, z>=0.


    2. Relevant equations
    It is bounded by x + y + z = 1. The transformations I need to use are x=u(1-v), y=uv(1-w), z=uvw.

    3. The attempt at a solution
    y+z = uv. J = uv(v-v^2+uv)
    So I get the integral (v-v^2+uv)dudvdw. But I don't know which bounds I need to use. Is this correct and how can I know the bounds?
     
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  3. May 18, 2017 #2

    BvU

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    Does the exercise text prescribe this ? Your problem statement doesn't -- could you please post the full problem statement ?

    For a start: If you can't write the bounds in terms of u, v and w, can you give them in terms of x, y and z ?
     
  4. May 18, 2017 #3

    Ray Vickson

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    If somebody is forcing you to use the transformation, then I guess you are stuck with it. However, just doing repeated integrations in terms of x, y, z is much more straighforward.
     
  5. May 18, 2017 #4

    SammyS

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    It's a good idea to include the whole problem statement in the main body of you post. If a part of the problem statement is contained in the thread title, please repeat that part in the body of the Original Post.

    Integral with transformations and bounded by x + y + z = 1


     
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