Convert a region into a rectangle

1. Mar 23, 2013

lyranger

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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

Last edited by a moderator: Mar 24, 2013
2. Mar 24, 2013

SammyS

Staff Emeritus
What specifically have you tried?

3. Mar 24, 2013

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 dunno the trick of findin proper v and u

4. Mar 24, 2013

SammyS

Staff Emeritus
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.