Given f(x,y,z)= use stokes theorem to determine the flux integral curlF dot ds, where S is the graph of z=9 - x^2 - y^2 for z=0 , oriented by the upward normal.

Question

Given f(x,y,z)=<y,z^2-x,x> use stokes theorem to determine the flux integral curlF dot ds, where S is the graph of z=9 - x^2 - y^2 for z>=0 , oriented by the upward normal.

please help!

Steve · Answer

It looks like this very problem is discussed at

http://tutorial.math.lamar.edu/Classes/CalcIII/StokesTheorem.aspx

f(x,y,z) is different, but the surface is a paraboloid just like yours. It goes through all the steps to evaluate the integral.

sam · Answer

thanks! I got it!! :D