(adsbygoogle = window.adsbygoogle || []).push({}); 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!

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# Homework Help: Solving for area using an integral (intro to parametric curves)

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