There is an example in my textbook which I´m having trouble with. The example is like this. " Find the area of the finite plane region bounded by the four parabolas, y=x^2 , y=2x^2 , x=y^2 , and x=3y^2 The region is called D. Let u=y/x^2 and v=x/y^2 The the region D corresponds to the rectangle R in the uv - plane given by 1≤ u ≤2 and 1≤ v ≤3 " The rest with the Jacobian determinant and so on I understand. What I don't understand in this example is the expression u=y/x^2 and v=x/y^2 I don't see why u and v are chosen this way. It would be great if someone could explain this to me.