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

Evaluate the surface integral

  
S

F · dS

for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x, y, z) = x i − z j + y k


S is the part of the sphere

x2 + y2 + z2 = 4

in the first octant, with orientation toward the origin

Math   Calculus   
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