Flux in open cylinder

Homework Statement

A vector field $$\vec{G}$$ in 3-space is defined outside the cylinder $$x^2 + y^2 = 4$$

$$\vec{G} = \frac{6y\vec{i}-6x\vec{j}}{x^2+y^2}$$

Find $$\int\limits_S \vec{G} \cdot · d\vec{A}$$ where S is the open cylinder $$x^2 + y^2 = 16 , 0 \leq z \leq 7$$ oriented outward.

The Attempt at a Solution

I am planning to use divergence theorem here... can I use it?

use also cilndric coordinates ;)

it's kind of hard to find the divergence here... is it just:

$$\frac{24xy}{(x^2+y^2)^2}$$

at least that's what I got. How do I parametrize the open cylinder?

What does it mean defined outside the cylinder?

What does it mean defined outside the cylinder?

I am actually confused my self with that... as far as my understanding goes it just means the direction points outwards...

someone care to correct me and give me more help to solve this problem?

Usually it mean that inside the cylinder and on its boundaries the field is null. Think about electrostatics ;)

MM