Question

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

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 = 81 in the first octant, with orientation toward the origin.

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