Stokes Theorem on a compound surface Consider the surface
Chapter 14, Problem 68(choose chapter or problem)
Stokes Theorem on a compound surface Consider the surface S consisting of the quarter-sphere x2 + y2 + z2 = a2, for z 0 and x 0, and the half-disk in the yz-plane y2 + z2 a2, for z 0. The boundary of S in the xy-plane is C, which consists of the semicircle x2 + y2 = a2, for x 0, and the line segment 3-a, a4 on the y-axis, with a counterclockwise orientation. Let F = 82z - y, x - z, y - 2x9. a. Describe the direction in which the normal vectors point on S. b. Evaluate AC F # dr. c. Evaluate 4S 1_ * F2 # n dS and check for agreement with part (b).
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