Convert a region into a rectangle

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Homework Help Overview

The problem involves expressing a region R, defined by the equation x^(3/2) + y^(3/2) = a^(3/2) in the first quadrant, as a double integral over a rectangle. Participants are exploring methods to find appropriate transformations for the variables involved.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants have attempted different variable transformations (u, v) to facilitate the integration but have encountered difficulties in finding suitable expressions. Questions about the effectiveness of their chosen transformations and the need for adjustments have been raised.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and questioning the validity of their approaches. Some guidance has been offered regarding potential transformations, but there is no clear consensus on the best method to proceed.

Contextual Notes

Participants are working under the constraints of the problem's requirements and are grappling with the complexities of the transformations needed for the double integral representation.

lyranger
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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
 
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lyranger said:
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?
 
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
 
Try [itex]\displaystyle u=x^{3/2}+y^{3/2} \,,\[/itex] and [itex]\displaystyle v=x^{3/2}-y^{3/2} \,,\[/itex]

You may have to do some tweaking on this.
 

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