Calculating Flux on a Curved Surface in Cylinder Coordinates

[kasse]

Homework Statement

The following vector field is given: F = < x + y^3, y, z - y^3 >

Let T be the solid given in cylinder coordinates by: r [0,1], tetha [0, pi], z [0, 2]

Find the flux out of the curved part of the surface of T.

2. The attempt at a solution

The normal vector n is < x, y, 0 >

F*n is therefore 1 + xy^3

Then I need dS = sqrt(1 + z_x² + z_y²) dx dy. Is this simply 1 dx dy?

 

[Dick]

But x and y aren't the variables you are going to integrate over, are they? Don't you want to integrate over theta and z? (You are sort of right, in the sense that dS is independent of the integration variables, if you choose them correctly).