Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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:
    x=a*cos[tex]^{3}[/tex][tex]\theta[/tex]
    y=a*sin[tex]^{3}[/tex][tex]\theta[/tex]

    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

    rock.freak667

    User Avatar
    Homework Helper

    Try the identity [itex]cos^2\theta+sin^2\theta =1[/itex]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook