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Homework Help: Integrals over a transformed region

  1. Nov 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider the change of variables x = x(u, v) = uv and y = y(u, v) =u^3+v^3

    Compute the area of the part of the x-y plane that is the transform of the unit square in the
    2nd quadrant of the u-v plane, which has one corner at the origin. (Since the transformation
    is 1:1 on the second quadrant (assignment 6), the area equals the integral over the square of
    the absolute value of the determinant of the Jacobian of the transformation.)

    3. The attempt at a solution
    So I computed the Jacobian to be 3v^3-3u^3. Then, since I just needed to integrate over a square, I did
    ∫[itex]^{1}_{0}[/itex]∫[itex]^{0}_{-1}[/itex] 3v[itex]^{3}[/itex]-3u[itex]^{3}[/itex] du dv. I keep getting 0 as an answer, but that just doesn't seem right, am I misunderstanding the question?

    also, sorry if my formatting is confusing, I don't really know how to make the integrals look pretty
  2. jcsd
  3. Nov 14, 2012 #2


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    I don't get zero. Try writing out the steps in more detail. I think you're getting a sign wrong.
  4. Nov 14, 2012 #3
    Wow...yea, i got a sign mixed up and ended up with .75-.75 instead of .75+.75. I got 1.5 as an answer, which sounds much more reasonable, thanks.
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