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I am supposed to evaluate

∫∫ e^(x+y)dA where the area of integration is given by the inequality |x|+|y|≤1.

So, suppose I do one of these Jacobians, and I set u = |x| and v = |y|, so wouldn’t the equation have to satisfy the inequality u+v≤1, and u≥0, v≥0? So, would wouldn’t the Jacobian be 1? But clearly I’m doing something wrong here, so any hints would be greatly appreciated!! Thanks!!