Originally Posted by

**angel.white** Use Stokes' Theorem to evaluate $\displaystyle \int_C \vec F \cdot d\vec r$. C is oriented counterclockwise as viewed from above.

$\displaystyle \vec F (x,y,z) = <x+y^2, y+z^2, z+x^2>$, 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 $\displaystyle \int_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot d\vec s$

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.