Change of variables for double integrals

[jonnyboy]

Homework Statement

Use a suitable change of variable to find the area of the region R bounded by y=x^2, y=4x^2, y=\sqrt{x}, y=\frac{1}{2}\sqrt{x}


2. The attempt at a solution
I am trying to first find the inverse transformations {u & v =?

 

[HallsofIvy]

Homework Statement

Use a suitable change of variable to find the area of the region R bounded by y=x^2, y=4x^2, y=\sqrt{x}, y=\frac{1}{2}\sqrt{x}


2. The attempt at a solution
I am trying to first find the inverse transformations {u & v =?

The obvious thing to do would be to set y= ux² and y= v\sqrt{x}= vx^1/2. That way, R is bounded by u= 1, u= 4, v= 1 and v= 1/2. u= y/x² and v= yx^-1/2.