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Change of variables: Factor

Problem

Suppose we wanted to evaluate the double integral
S=Dxydxdy
by first applying a change of variables from D to R:
x=X1(u,v)=euvy=X2(u,v)=eu+v
What is S under the change of variables?
If you know an expression within absolute value is non-negative, do not use absolute value at all.
S=R
dudv
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