(Step-by-Step) Use the change of variables x=1/2(u+v), y=1/2(u-v) to find the exact value of the double integral I=∫_R(x+y) e^z^2-y^2 d x d y where R is
Question: Use the change of variables \(x=\frac{1}{2}(u+v), y=\frac{1}{2}(u-v)\) to find the exact value of the double integral
\[I=\iint_{R}(x+y) e^{z^{2}-y^{2}} d x d y\]where \(R\) is the rectangle bounded by the lines \(y=\pm x, y=3-x\) and \(y=x-2\).
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