Help me Vector Calculus Stumped on how to do these problems

[davidson89]

1) Let S be the first-octant portion of the paraboloid z = x^2 + y^2 that is cut off by the plane z=4. If F(x,y,z) = (x^2 + z)i + (y^2z)j + (x^2 + y^2 + z)k , find the flux of F through S.

2) Let S be the surface of the region bounded by the coordinate planes and the planes x + 2z = 4 and y = 2. Use the Divergence Theorem to the flux of F(x,y,z) = (2xz)i + (xyz)j + (yz)k through S.

I am really having trouble setting up the integrals to answering these questions. If you could help me set it up and help me find the flux then much would be appreciated. If you could explain step by step to any of these questions i would be very thankful. THANKS

 

[Defennder]

Well what have you tried for them?

1. The standard way of doing these surface integrals is to first parametrise the surface S, then next expressing the vector field in terms of the parametrisation. Then you find the dot product of the vector field with the normal vector and perform the double integration over the surface.

2. What does the divergence theorem say and how do you use it?