Question

PLEASE HELP!!!!!
Find the flux of F={xz,x^2y,y^2z} through the surface made of the cylinder x^2+y^2=1, paraboloid z=x^2+y^2, and the coordinate planes.

Answer 1

what have you tried ?

Answer 2

I've tried finding the flux by taking the partials of vectorF.
I have an example we did in class we are working off that has an open ended cylinder. I don't know how to work with both the cylinder and parabolid

Answer 3

Okay, can we use divergence theorem ?

Answer 4

yes. if we assume xz(i)+x^2y(j)+y^2z(k)

Answer 5

which would give z+x^2+y^2=?

Answer 6

@ganeshie8

Answer 7

yes set up the triple integral

Answer 8

\[\int\limits_{0}^{2\pi}\int\limits_{?}^{?}\int\limits_{?}^{?} (???) r dzdrd \theta\]
this is where i get lost @ganeshie8

Answer 9

you want the flux only in first octant i think

Answer 10

\(\theta\) : 0->pi/2

Answer 11

okay and how do I find what r is?

Answer 12

r : 0->1

Answer 13

would you mind explaining why?

Answer 14

the shadow of the solid region between xy plane, cylinder and paraboloid gives you a disk of radius 1