I am working on the surface integral - flux section. I feel so desperate. Looking at the book for two days,still can't conclude how to solve this kind of questions.
I don't quiet get the idea of this section for how to compute the flux. It seems that we need to memories many formulas in order to solve flux question given in the form of z=g(x,y), y=g(x,z) or x= g(y,z).
I am just wondering can anyone give me a simple conclusion or lecture of how to solve flux questions.
Also, please help me for the following questions.
Evaluate the flux of the vector field F(x,y, z) = -yi + xj -zk
through the unit sphere x^2 + y^2 +z^2 =1 that has downward orientation.
Evaluate the flux of the vector field F (x,y,z) = <x, -1, z> through the surface S that has downward orientation and given by the equation z=xcosy where 0<or = x < or =1, pi/4 < or = y < or = pi/3.