Question

Can someone help with the set up of this?
Find the flux of the vector field F=(5x-y)i-2yj+7yzk out of the region W which is defined by the surfaces x=y^2, x=4, z=0, and x=z

Answer 1

Well, to calculate flux, we can do the integral:

\[\int\limits del . F(x,y,z) dA\]
(sorry, there doesn't seem to be a del symbol available, and that's a dot product between del and F. You may know it as "divergence")

Do you know how to use this?

Answer 2

My main problem is trying to set up the parameterization, i don't know if there is a way to do it with just one. Also, looking at the surface, it is akward to try and figure out the bounds for u and v.

Answer 3

I made a mistake, anyway. Integral should be over dV :)

Answer 4

We can use the Divergence Theorem to change the integral to one over an area.

Can you show me exactly where you're at in the whole process?

Answer 5

I have the integral for the first surface, the flat vertical one, \[\int\limits_{0}^{4}\int\limits_{-2}^{2}(20-u) du dv = 320\] Which I think is right....but not totally sure.

Answer 6

Hmm, trying to see exactly what you did.

Answer 7

I had the parameterization \[\Phi(u,v)=<4,u,v> \] with u from -2 to 2 and v from 0 to 4. then I took the div of F to be 5-2+7y and substituted in u for y, then took the dot product of that and the cross product of \[\Phi _{u} and \Phi _{v}\]

Answer 8

Ah, I see. I'll be honest, I'm rusty with approaches like this. I'd probably advise trying to get a hold of someone who is less rusty. : /

Answer 9

Thanks, I figured out that I was doing it wrong anyways.

Answer 10

Trying to get someone else for you, all the same :)