Convert a region into a rectangle

[lyranger]

Homework Statement

Let R be the region bounded by x^3/2+y^3/2=a^3/2 (x>0, y>0) and the coordinate axes x=0, y=0. Express it in double integral over a rectangle.

Homework Equations

The Attempt at a Solution

How to solve this people please?

I tried a couples time but failed to find v u which is essential to solving this problem as all we have to do is find ∂(u,v)/∂(x,y)

cheers

 

[SammyS]

let R be the region bounded by x^3/2+y^3/2=a^3/2 (x>0, y>0) and the coordinate axes x=0 y=0 express it in double integral over a rectangle
how to solve this people please

I tried a couples time but failed to find v u which is essential to solving this problem as all we have to do is finding ∂(u,v)/∂(x,y)

cheers

What specifically have you tried?

 

[lyranger]

let u=y/(a^1.5-x^1.5)^2/3 and v=x/(a^1.5-y^1.5)^2/3
got 0 for this
let u=y/(a^1.5-x^1.5)^2/3 and v=x/y this got really nasty
so i just don't know the trick of findin proper v and u

 

[SammyS]

Try \displaystyle u=x^{3/2}+y^{3/2} \,,\ and \displaystyle v=x^{3/2}-y^{3/2} \,,\

You may have to do some tweaking on this.