Verify Stokes' theorem
∫c F • t ds = ∫∫s n ∇ × F dS
in each of the following cases:
(a) F=i z2 + j y2
C, the square of side 1 lying in the x,z-plane and directed as shown
S, the five squares S1, S2, S3, S4, S5 as shown in the figure.
(b) F = iy + jz + kx
C, the three quarter circle arcs C1, C2, and C3 directed as shown in the figure.
S, the octant of the sphere x2 + y2 + z2 = 1 enclosed by the three arcs.
(c) F = iy - jx + kz
C, the circle of radius R lying in the xy-plae, centered at (0,0,0) and directed as shown in the figure.
S, the curved upper surfaces of the cylinder of radius R and height h.
∫c F • t ds = ∫∫s n ∇ × F dS Stokes' theorem
The Attempt at a Solution
I have been staring at this problem for two weeks and every time I think i get it, i find out I'm wrong. Please help!