Question

Let S be the disk { (x,y,z) such that (x-1)^2 +(z-2)^2 =9 , y=17}, and let C be the boundary of S oriented counterclockwise if viewed from the top of the positive y-axis. Suppose F(x,y,z)= f(x,y,z)i + g(x,y,z)j + h(x,y,z)k, where f and g and h have continuous first partial. Also assume fsubz=hsubx

thoughout some open set containing S.

Prove that the integral of C (closed) F dot T ds =0.

Thank you