Evaluate the double integral over sigma of (F*n dS) in the following cases, Use Gauss' Theorem and/or symmetry whenever convenient c) F =

Evaluate the double integral over sigma of (F*n dS) in the following cases, Use Gauss' Theorem and/or symmetry whenever convenientc) F = gradient(f), f(x,y,z) = xyz+5, sigma is the sphere x^2+y^2+z^2=9, n is the outward normal

f(x,y,z)= xyz +5F = gradient (f)So, F = (xyz + 5)î + (xyz + 5)ĵ = yz î + xz ĵ + xy k̂ And ,here S is x² + y² + z² =9 + (xyz + 5) k̂ According to divergence theorem of Gauss, =S V =...