Question: Verify that the line integral and the surface integral of Stokes Theorem are equal for the following vector fields, surfaces S, and closed curves C.

Verify that the line integral and the surface integral of Stokes’ Theorem are equal for the following vector fields, surfaces S, and closed curves C. Assume that C has counterclockwise orientation and S has a consistent orientation.


F = (0, -x, y); x + y + z2: = S

F = (0, -x, y); x + y + z2: = S is the upper half of the sphere 4 and C is the circle x + y = 4 in the xy-plane.

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