Change of variables in double integrals textbook problem

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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.

 

[0rthodontist]

When u = y/x^2, y = u*x^2 and when v = x/y^2, x = v*y^2. So for example when y ranges from x^2 to 2x^2, u ranges from 1 to 2.

 

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I understand this better now.
Thanks