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How do I calculate this double integral using a change of variables?

  1. Dec 13, 2013 #1
    The problem is as follows.

    Calculate the double integral of cos ((x-y)/(x+y)) dA over R, where R is the triangle bounded by the points (0,0), (2,2), and (2 + pi, 2 - pi).

    I understand that you have to set U = x-y and V = x+y. However, I am having a hard time finding the bounds on the integral because the slope of the lines isn't 1. I can't simply add x to the other side of each equation because of the 2+pi and 2-pi. Any help would be appreciated. Thanks!
  2. jcsd
  3. Dec 13, 2013 #2


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    Gold Member

    It is a case of mapping the coordinates of the points in Cartesians to uv space. When x=y=0, what are u and v? When x=y=2, what are u and v? Similarly, for x,y=2±π. Once you have pairs (u,v), you can sketch the resulting region and then determine the bounds for u and v.
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