(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use a line integral to find the area of the region enclosed by astroid

x = acos^{3}[tex]\phi[/tex]

y = asin^{3}[tex]\phi[/tex]

0 [tex]\leq \phi \leq 2\pi[/tex]

2. Relevant equations

I used Green's Theorem:

[tex] \oint_C xdy - ydx[/tex]

3. The attempt at a solution

I solved for dx and dy from my parametric equations. I then plugged in x, y, dx, and dy into the integral to solve for the area.

After simplifying, I came out with:

[tex] \frac {3a}{2} \int_0^{2\pi} cos^2\phi sin^2\phi d\phi[/tex]

Now in order to solve this, I used a half angle formula, [tex]cos\phi sin\phi = (\frac{1}{2}sin2\phi)^2 = \frac {1}{4}sin^2 2\phi [/tex]

Which then I used a different angle formula to get:[tex] \frac{1}{8}(1-cos4\phi)[/tex]

Am I on the right track? I would then integrate to solve...

The latex on my computer isnt working, but hopefully its working on everyone else's?

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# Homework Help: Using Green's Theorem

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