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

find the region enclosed by astroid

x= acosϑ^{3}

y=asinϑ^{3}

the astroid looks like this picture in my book, with the shaded region stretching for x (-a,a)

and for y(-a,a)

2. Relevant equations

i think the formula is ..... from (-a to a) ∫ y * x' dϑ

3. The attempt at a solution

a = ∫ acosϑ^{3}* 3asinϑ^{2}cosϑ

a = 3a^{2}∫ cosϑ^{4}* sinϑ^{2}

a = 3a^{2}∫ cosϑ^{4}* (1-cosϑ^{2})

a = 3a^{2}∫ cosϑ^{4}- cosϑ^{6}

is this one the right track, if so I can evaluate the rest of that integral myself

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# Find the area of region enclosed by astroid

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