Exercise
Let E be the bounded area between the XY plane and the surface
z=4−x2−y2
Let S be the surface area of E.
Calculate the integral
∫∫SF⋅n^ds
Or in another notation
∫∫SF⋅NdA
Where the vector field F is
F=(xzsin(yz)+x3,cos(yz),3zy2−ex2+y2)
Final Answer
∫∫SF⋅n^ds=32π
Solution
Coming soon…