1. The problem statement, all variables and given/known data What is the line Integral of the function f = yi-xj+zk (where i,j,k, are cartesian unit vectors) around a circle with radius R centered at the origin? 2. Relevant equations Stokes Theorem: i.e. the integreal of some function between a and b is equal to the difference in the values of the antiderivitive of that function evaluated at a and b. 3. The attempt at a solution As I understand it, the answer should be zero; since the integral is over a closed circle (and since it is a continuous function with no sigularities). In this case, a=b, so the antiderivitive of f at a minus the anti-derivitive of f at b = 0. antiderivitive of f: F= .5(y^2)i-.5(x^2)j+.5(z^2)k Limits of integration: a=b Apply Stokes Theorem:F(a)-F(b) =0 However, apparently the answer is 2*pi*(R^2) (the area of a circle). No explenation is given except that stokes theorem should be used . Any Ideas? I am almost certain there is an error in the solutiuons, but I would appreciate a second opinion.