Use Stokes' Theorem to Evaluate $\int _ { C } x y d x + y z d y + z x d z$

Short Answer

Use Stokes' Theorem to evaluate $\int _ { C } x y d x + y z d y + z x d z$ , where C is the triangle with vertices $( 1,0,0 ) , ( 0,1,0 )$ , and $( 0,0,1 )$ , oriented counterclockwise as viewed from above.