Let vector Fx y gx y hx y be a differentiable twodimensiona

Let vector F(x, y) = (g(x, y), h(x, y)) be a differentiable two-dimensional vector in R^2, and C R^2 a closed, simple, smooth planar curve, with local unit normal vector hat N (oriented in the outward direction away from the domain D whose boundary C is), and arclength element dl. Prove the two-dimensional version of the divergence theorem,

Solution

Here Gauss divergence theorem is used.