Originally Posted by

**Nguyen** Hey,

Let $\displaystyle f(x,y) = ln(x^2 +y^2)$

Let C be the circle $\displaystyle x^2 + y^2 =a^2$ with $\displaystyle a^2 \ne 0 $

and evaluate the flux integral:

$\displaystyle \oint_C\nabla f \cdot n ds$

I can't seem to use Greens Theorem on this particular question and don't know why.

Second part:

Now let K be an arbitrary simple closed curve in the plane that does not pass through

(0,0). Use Green's theorem to show that:

$\displaystyle \oint_K\nabla f \cdot n ds$

has, only, two possible values depending on whether (0,0) lies inside or outside of K.

I really need help on this one.

Can someone help me with this?

Thanks