Does this thread help: http://www.mathhelpforum.com/math-he...s-theorem.html
By the way, your curl and equation for the plane look OK.
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)
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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.
Does this thread help: http://www.mathhelpforum.com/math-he...s-theorem.html
By the way, your curl and equation for the plane look OK.
is an infinitesimal element of directed surface.
where is a unit normal vector to S.
The formulae I quote in the other thread follow from this.
For your surface (plane), . Then:
where I've substituted .
The region of integration in the xy-plane is clearly the right-triangle with vertices at (0, 0), (1, 0) and (0, 1).
So your line integral is simply twice the area of this triangle: 1.