Question

proof problem see attachment...

Answer 1

@experimentX

Answer 2

Refer to Green's theorem.
your theorem 2 states that, if M, N, M_y, N_x are continuous on the region R, and M_y = N_x, then there exists a function U(x,y) such that U_x = M and U_y = M.

It follows from the definition of exact equation.

Answer 3

Now come to Green's theorem,