Use Stokes' Theorem to evaluate . C is oriented counterclockwise as viewed from above.
, C is the triangle with vertices (1,0,0), (0,1,0), and (0,0,1)
I've computed the curl as <-2z, -2x, -2y> and the equation of the plane as z=1-x-y
Stokes' theorem says
But I can't figure out how to evaluate the second part, since the curl is a vector, and the surface has three variables, I don't know how to get it into a form I can integrate.