# Find the outward flux of the field - Green's Theorem

1. Nov 8, 2007

### mit_hacker

1. The problem statement, all variables and given/known data

(Q) Find the outward flux of the field

F=(3xy-x/(1+y^2 ))i+(e^x+tan^(-1)⁡y )j

across the cardioid r=a(1+cos⁡θ), a>0.

2. Relevant equations

div F = (∂M )/∂x+∂N/∂y

3. The attempt at a solution

I could easily set up the double integral which is:

∬▒3 r^2 sin⁡θ dA

However, I am unsure as to how to determine the limits to be used.

2. Nov 8, 2007

### HallsofIvy

Staff Emeritus
?? The limits of integration ARE the cardioid, of course: $\theta$ going from 0 to $2\pi$, r from 0 to a(1+ cos($\theta$)). Since that is given in polar coordinates, it might be best to convert div F to polar coordinates.

3. Nov 8, 2007

### mit_hacker

Yes but.....

Usually, the limits of r ranges from a constant value to another constant value of r. Why do we, in this case simply plug in the equation of the cardioid?

Thanks a lot for your help and support!!!!