Let S be the surface given by the graph z = 4 - x^2 - y^2 above the xy-plane (that it is, where z \(\displaystyle \geq\) 0) with downward pointing normal, and let
F (x,y,z) = xcosz i - ycosz j + (x^2 + y^2 ) k
Compute \(\displaystyle \oint\)\(\displaystyle \oint\) F dS. (F has a downward pointing normal)
(Hint: Its easy to see that div F = 0 on all R^3. This implies that there exists a vector field G such that F = Curl G, although it doesnt tell you what G is)
My daughter is struggling to do this problem. I would really appreciate it if you could show some steps in the solution. You dont need to show how you did the integration steps but just how you arrived at the answer. Please, your help is greatly appreciated. Help me help my daughter!
F (x,y,z) = xcosz i - ycosz j + (x^2 + y^2 ) k
Compute \(\displaystyle \oint\)\(\displaystyle \oint\) F dS. (F has a downward pointing normal)
(Hint: Its easy to see that div F = 0 on all R^3. This implies that there exists a vector field G such that F = Curl G, although it doesnt tell you what G is)
My daughter is struggling to do this problem. I would really appreciate it if you could show some steps in the solution. You dont need to show how you did the integration steps but just how you arrived at the answer. Please, your help is greatly appreciated. Help me help my daughter!