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Homework Statement
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.
Homework Equations
None
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] 1/2Can anyone show me how to figure this problem out without any reference to graphing (just
pure algebraic)?