I need to show the Gaussian integration theorem for a rectangle R = ]a, b[ x ]c, d[ in the two-dimensional real numbers.
I have seen many examples using a vector field and calculating the divergence from these field. But the problem I have to solve, doesn't has any given vector field.
How can I show the equality of the two integrals in the Gaussian integration theorem without having concrete values? I was asked to show the iterated integrals directly, but I don't understand exactly what it means.
Kindly regards