0
$\begingroup$

enter image description here

Hello friends!

I've tried using the typical variable change $u = x+y$ and $v = x-y$ but this gives you a determinant of 1/2, which doesn't let you prove the equality.

PD: For those that can't read spanish the picture says: find $D \epsilon R^2$ so that the equation is true for every pair of continuous functions $f$ and $g$

  • 1
    You've got the right change of variable; the question is "If $[0, 1] \times [0, 1]$ is the domain of integration on the right, what's the domain $D$ of integration on the left?" – 2017-02-19
  • 0
    Well, with that change of variables D would be the "diamond" of vertices (0,0), (1,1), (1/2, -1/2), (1/2, 1/2). But that still doesn't give an answer to how to remove the 1/2 factor that would appear on the right side of the equation – 2017-02-19
  • 0
    What's the area of that diamond? – 2017-02-19
  • 0
    It just cannot be done. – 2017-02-19

0 Answers 0