(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let D be the region y [tex]\leq[/tex] x [tex]\leq[/tex] 1 and 0 [tex]\leq[/tex] y [tex]\leq[/tex] 1.

Find the boundaries of the integration for the change of variables u and v, if:

x = u + v and y = u-v.

2. Relevant equations

None

3. The attempt at a solution

I solved for u and for v in terms of x and y.

u = [tex]\frac{x+y}{2}[/tex]

v = [tex]\frac{x-y}{2}[/tex]

Then I got stuck.

The book answer's is:

v [tex]\leq[/tex] u [tex]\leq[/tex] 1-v and 0 [tex]\leq[/tex] v [tex]\leq[/tex] 1/2

Can anyone show me how to figure this problem out without any reference to graphing (just

pure algebraic)?

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# Homework Help: Change of Variables in Multple Integrals

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