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Jacobean Problem

  1. Nov 29, 2011 #1
    1. The problem statement, all variables and given/known data
    I'm also having trouble with this Jacobean problem. I really could use some help:

    Evaluate ∫∫(x+y)dxdy over y=x,y=x-5,y=-x,x+y=5

    2. Relevant equations

    3. The attempt at a solution

    I know that if I can get u and v correct this becomes a simple integral, but I have no idea what to make u and v and how to set my limits
  2. jcsd
  3. Nov 29, 2011 #2


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    Take a wild guess. Express your limit conditions by moving all of the x's and y's to one side and the constants to the other. What sort of expressions do you see on the x and y side?
  4. Nov 30, 2011 #3


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    The boundary of the region are parallel straight lines. In fact, they are at right angles so this is a rectangle. You want to change it to a rectangle with sides along the coordinate axes. So define u and v so that the equations of the sides become u= constant and v= constant. That is what Dick is suggesting you do.
  5. Nov 30, 2011 #4
    so if I am understanding correctly, y-x=5 and x+y=5 therefore setting u=x+y and v=y-x so that u=5 and v=5, but how do i prove that the other sides of the rectangle are x=0 and y=0 (or u=0 and v=0)
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