# Area of a polar function

1. Oct 6, 2008

### tomcochrane

1. The problem statement, all variables and given/known data
I'm trying to find the area enclosed by the polar curve $$r^2 = 2-cos(r*cos(\theta))*sin(r*sin(\theta))$$.

2. Relevant equations

I've been trying to use the polar area formula, $$A= \frac{1}{2}\int _a ^b r^2 d\theta$$, where r is a function of $$\theta$$

3. The attempt at a solution

I'm using Maple, and it's getting a little messy. First I had to plot the function, and that was fine. For the plot I used r goes from -2 to 2 and $$\theta$$ goes from 0 to $$\pi$$. That was fine.

Now I have to find the area of the plot. I tried getting the r's and theta's onto seperate sides of the equation, so I could put r into the area integral, but you could imagine that would be a huge mess. I must be forgetting something. Where should I go from there? Or am I missing something and heading in the wrong direction? Thanks.