Chapter 14.4, Problem 63E

Flux integrals Assume the vector field F = (f, g) is source free (zero divergence) with stream function ψ. Let C be any smooth simple curve from A to the distinct point B. Show that the flux integral ${\displaystyle {\int }_{C}F\cdot nds}$ is independent of path; that is, ${\displaystyle {\int }_{C}F\cdot nds}=\psi \left(B\right)-\psi \left(A\right)$.