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Solving for area using an integral (intro to parametric curves)

  1. Oct 27, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the area of the region enclosed by the asteroid:

    2. Relevant equations
    A = [tex]\int[/tex][tex]\sqrt{\frac{dy}{d\theta}^{2}}+\frac{dx}{d\theta}^{2}[/tex]

    3. The attempt at a solution
    [tex]\frac{dy}{d\theta}[/tex] = 3asin[tex]^{2}\theta(cos\theta)[/tex]
    [tex]\frac{dx}{d\theta}[/tex] = -3acos[tex]^{2}\theta(sin\theta)[/tex]

    Plugging that into the equation, I just cannot simplify this integral (sorry ... I tried to write it out but the code got beyond messed up!!) from 0 to pi/2! I square them but cannot combine them. Is there an easy way to factor it? Any help you could offer would be greatly appreciated!
  2. jcsd
  3. Oct 27, 2008 #2


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    Homework Helper

    Try the identity [itex]cos^2\theta+sin^2\theta =1[/itex]
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