I'm currently trying to understand the reasoning for an output that was produced using Gauss Green on Parametric Regions.
Say f(x,y) = 3-x+y and g(x,y) = 3-x. These functions plot surfaces above the region parameterized as x[t_] = Cos[t] (1 - Cos[t]) & y[t_] = Sin[t] (1 - Cos[t]) . When I used Gauss Green i obtained a value of 18.0642 for both f(x,y) & g(x,y). The only major difference between f(x,y) & g(x,y) is the exclusion of y in g(x,y) = 3-x. Although they are both above the same parameterized region, how do they both produce the same value when using Gauss-Green? What am I missing here?