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Double integral xy to uv

  1. Dec 9, 2011 #1
    1. The problem statement, all variables and given/known data
    function inside is (x+y)^2 * sin(x^2 - y^2)
    R is the triangular region w/ vertices (0,0) , (0,2) , (1,1)

    x = (u+v)/2
    y = (v-u)/2

    What are the correct limits ??

    3. The attempt at a solution
    Also, when plugging in x and y in the function, i ended up getting (v^2)*(sin(uv)). is that right? for the limits, i have no idea, all my attempts failed =/
  2. jcsd
  3. Dec 9, 2011 #2


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    There are three boundary lines, x= 0, from (0, 0) to (0, 2), y= x, from (0, 0) to (1, 1), and y= 1- x, from (0, 2) to (1, 1). x= (u+ v)/2= 0 gives u+ v= 0 so v= -u. y= x gives (v- u)/2= (u+ v)/2 so ...
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