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Finding the area of one loop of the lemniscate

  1. Nov 20, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the area of the region bounded by one loop of the lemniscate r2 = a2sin(2θ) with a > 0 using double integration.


    2. Relevant equations



    3. The attempt at a solution

    I was able to figure out the limits of integration for theta (0 to ∏/2), but what would my limits be for r?
     
  2. jcsd
  3. Nov 20, 2012 #2

    haruspex

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    The limits for r will be functions of theta. Integrate wrt r first. When you plug in the limits, those functions will come into the integrand. Then you can integrate wrt theta.
     
  4. Nov 20, 2012 #3
    I'm sorry, I really don't understand. How can I integrate wrt r without setting the limits of my integrand first? What would those limits be?
     
  5. Nov 20, 2012 #4

    LCKurtz

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    When you integrate in the r direction, r goes from r = 0 to the r on the curve, which is a function of ##\theta##.
     
  6. Nov 20, 2012 #5

    haruspex

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    For a given value of theta, what is the smallest value of r within the region? What is the largest value with the region?
     
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