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