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Area of a polar function

  1. Oct 6, 2008 #1
    1. The problem statement, all variables and given/known data
    I'm trying to find the area enclosed by the polar curve [tex]r^2 = 2-cos(r*cos(\theta))*sin(r*sin(\theta))[/tex].

    2. Relevant equations

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

    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 [tex]\theta[/tex] goes from 0 to [tex]\pi[/tex]. 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.
  2. jcsd
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