Let F(x,y,z)=2z2xi+(23y3+tan(z))j+(2x2z−1y2)k. Use the Divergence Theorem to evaluate ∫SF⋅ dS where S is the top half of the sphere x2+y2+z2=1 oriented upwards. ∫∫SF⋅ dS=

Question

Let F(x,y,z)=2z2xi+(23y3+tan(z))j+(2x2z−1y2)kF(x,y,z)=2z2xi+(23y3+tan⁡(z))j+(2x2z−1y2)k. Use the Divergence Theorem to evaluate ∫SF⋅ dS∫SF⋅ dS where SS is the top half of the sphere x2+y2+z2=1x2+y2+z2=1 oriented upwards.

∫∫SF⋅ dS=

Answer 1

I’m not sure I got this right, but the above photo shows my working. Because of all the mathematical symbols I thought it would be better to use a photo because comms devices vary in what symbols will display. I hope the answer is helpful.