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Change of variables: Factor


Suppose we wanted to evaluate the double integral
S, equals, \iint, start subscript, D, end subscript, x, minus, y, d, x, d, y
by first applying a change of variables from D to R:
x=X1(u,v)=euvy=X2(u,v)=eu+v\begin{aligned} x &= X_1(u, v) = e^u - v \\ \\ y &= X_2(u, v) = e^u + v \end{aligned}
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, equals, \iint, start subscript, R, end subscript
d, u, d, v