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 [–a, a] on the y-axis, with a counterclockwise orientation. Let F = 〈2z – y, x – z, y – 2x〉.
a. Describe the direction in which the normal
b. Evaluate
c. Evaluate
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