Another question I'm having trouble with is:
"Find the flux of F(x,y,z) = -yi + xj + (6z^2)k out of the closed surface S, bounded by the paraboloids z = 4 - x^2 - y^2 and z = x^2 + y^2."
I can get the graph drawn easily enough, I just can't figure out what the limits of my integration should be.
Any assistance would be much appreciated.
This may sound dumb, but can I break this into two separate flux integrals? Since they are two paraboloids that meet at z=2, is that a good way to go about it?
And I'm thinking the top paraboloid would be "oriented upward" and the bottom paraboloid would be "oriented downward", yes?