According to my professor, this formula is called the integral formula of Gauss and Green. I've tried searching for it online but I could find nothing similar to it.
B here is a region that's bounded by the simple closed curve γ(t).
I don't really understand what is it that we get after applying this formula. I mean, when we calculate the definite integral of f over the Intervall [a,b], we get the area under the curve of f from x=a to x=b. And double integrals are used either to calculate the area of a region or the volume above it that's bounded by the surface of a multi-variable function. But what is it that we calculate using this formula?
This formula is supposed to be something slimier to the fundamental theorem of calculus but in multi-variable calculus. I cannot see how.
Thanks for all your help. And forgive me for the grammatical mistakes, if there is any. English isn't my first language.