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Evaluate the surface integral    S F · dS for the given vector field F and the oriented surface S....

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Question

Basic Math

Evaluate the surface integral

  
S

F · dS

for the given vector field F and the orientedsurface S. In other words, find the flux ofF across S. For closed surfaces, use thepositive (outward) orientation.

F(x, y, z) = x i − z j + y k


S is the part of the sphere

x2 + y2 + z2 = 9

in the first octant, with orientation toward the origin

Answer & Explanation Solved by verified expert
3.6 Ratings (461 Votes)
Solution we have x2y2z2 9 Solving the equation of the sphere S for z we get z 9 x2 y2 Since were considering the first octant only all the points are    See Answer
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