# Thread: Green's wih polar coordinates!! :(

1. ## Green's wih polar coordinates!! :(

Use Green's theorem o find the counterclockwise circulation and outward flux for the field F and curve C:

F=(arctan(y/x))i + ln(x^2+y^2)j
C: The boundary of the region defined by the polar coordinate inequalities
r between 1 and 2
theta between 0 and pi

I know the formulas for greens, I'm just confused how to handle this with the polar coordinate boundary.

2. Originally Posted by s7b

Use Green's theorem o find the counterclockwise circulation and outward flux for the field F and curve C:

F=(arctan(y/x))i + ln(x^2+y^2)j
C: The boundary of the region defined by the polar coordinate inequalities
r between 1 and 2
theta between 0 and pi

I know the formulas for greens, I'm just confused how to handle this with the polar coordinate boundary.
Note that the region of integration is the area between the top half two circles

$\displaystyle x^2+y^2=4$ and $\displaystyle x^2+y^2=1$

using greens theorem we should get

$\displaystyle \int _{D} \int \frac{x}{x^2+y^2}dA$

but this will be much easier to integrate in polar coordinates so

$\displaystyle \int_{0}^{\pi}\int_{1}^{2} \frac{r\cos(\theta)}{r^2}rdrd\theta=\int_{0}^{\pi} \int_{1}^{2}\cos(\theta)drd\theta$

3. is this result simply 0....

4. Originally Posted by s7b
is this result simply 0....
That is what I got for the value of the integral