How do I solve this?
Calculate the circulation, in two ways, directly and using Stokes' Theorem. The vector field.
Calculating directly, we break C into three paths. For each, give a parameterization that traverses the path from start to end for 0 < t < 1. On C from 0, 0, 0 to 7, 0, 0, F(t) < 7, 0, 0 >. On C from 7, 0, 0 to 7, 6, 0, 7 < 0, 6, 0 >. On C from 7, 6, 0 to 0, 0, 0, t.
So that integrating we have Fdr fcp.dr =
pospue Using Stokes' Theorem, we have curlF = So that the surface integral on S, the triangular region on the plane enclosed by the indicated triangle, is scurlPdA = Sdydx where a = b = c = and d = Integrating, we get fF-dr = scurlPdA