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Change of variables

  1. Aug 11, 2008 #1
    1. The problem statement, all variables and given/known data
    Evaluate the double integral over R of cos[(y-x)/(y+x)] dA where R is the trapezoidal region with vertices (1,0) (2,0) (0,1) and (0,2).


    3. The attempt at a solution

    First I set u=y-x, v=y+x. I have 4 sides in the xy-plane that need to be transformed into the uv-plane. Side 1 is y=-x+2, Side 2 is y=-x+1, and then Side 3 & 4 are 0<x<2 (where the less than sign signifies less than or equal to).

    I solved for v, and got v=1, v=2, so I have those limits. But I can't figure out how to find the limits for u.
     
  2. jcsd
  3. Aug 11, 2008 #2
    u+v = 2y
    u-v = -2x

    using x = 0, y =y and x =x, y = 0

    you can get u = v and u = -v

    I don't know better method to find these limits
     
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