Let be the closed curve that is the boundary of the triangle with vertices at the points and .
Specify a direction along and consider the integral
where . Explain why the contribution to the integral is the same from each edge of , and evaluate the integral.
State Stokes's theorem and use it to evaluate the surface integral
the components of the normal to being positive.
Show that in the above surface integral can be written in the form .
Use this to verify your result by a direct calculation of the surface integral.