題組內容

7. Let S be the part of the graph

z = cosxsiny 0≤x≤,0≤y≤π,

with upward orientation. Consider the vector field F(x, y, z) = zi + yzk.

(b) Let C be the boundary curve of S. Decompose C as the union of differentiable parametric curves and evaluate F.dr directly. Show that the line integral equals JC the surface integral in part (a) which is consistent with Stokes' Theorem