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Change of variables in double integrals textbook problem

  1. Mar 21, 2006 #1
    There is an example in my textbook which I´m having trouble with.

    The example is like this.
    "
    Find the area of the finite plane region bounded by the four parabolas, y=x^2 , y=2x^2 , x=y^2 , and x=3y^2
    The region is called D.

    Let u=y/x^2 and v=x/y^2

    The the region D corresponds to the rectangle R in the uv - plane given by
    1≤ u ≤2 and 1≤ v ≤3
    "
    The rest with the Jacobian determinant and so on I understand.

    What I don't understand in this example is the expression
    u=y/x^2 and v=x/y^2
    I don't see why u and v are chosen this way.
    It would be great if someone could explain this to me.
     
  2. jcsd
  3. Mar 21, 2006 #2

    0rthodontist

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    Science Advisor

    When u = y/x^2, y = u*x^2 and when v = x/y^2, x = v*y^2. So for example when y ranges from x^2 to 2x^2, u ranges from 1 to 2.
     
  4. Mar 22, 2006 #3
    I understand this better now.
    Thanks
     
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