Find the flux (calculus problem)?

[mjf67089]

Homework Statement

The directions for this calculus problem say find the flux of F across surface S (that is find the double integral F (ds)) where F = (x,2y,z), S is the part of the cone (x^2+z^2)^1/2=y inside of the cylinder x^2+z^2=1 and n points to the right.

Homework Equations

I'm pretty sure you need to use the divergence theorem here. So I guess ∫∫s F · dS is a relevant equation.

The Attempt at a Solution

Here is my work, along with the answer that I got. Please tell me if it is right.

∫∫s F · dS
= ∫∫∫ div F dV
= ∫∫∫ (1 + 2 + 1) dV
= 4 ∫∫∫ dV.

Now, convert this to cylindrical coordinates (with y playing the role of z):
4 ∫(θ = 0 to 2π) ∫(r = 0 to 1) ∫(y = 0 to r) r dy dr dθ
= 4 * 2π ∫(r = 0 to 1) r^2 dr
= 8π/3.

 

[LCKurtz]

The divergence theorem applies to flux outward from a closed volume. You haven't mentioned anything about the base(s) of the cone. Also, in that case the outward direction wouldn't be to the right.

Perhaps you are meant to calculate the flux directly. And how about the part of the cone where y < 0, is that included?

An exact statement of the problem is needed to know what you are actually trying to calculate.