Please see the attached file for the fully formatted problem.
A spherical surface K is given by the equation x^2+y^2+z^2=25
Let S be part of the spherical surface above the plane z=4
calculate the double plane integral over S of F.n where F = y^2-xz, x^2-yz, z^2-xy and n is teh unit vector to the surface S with positive third coordinate.© BrainMass Inc. brainmass.com March 4, 2021, 9:23 pm ad1c9bdddf
The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word ...
The solution (4-pages) shows how the integral can be solved using a nifty trick (the divergence theorem).