anonymous
  • anonymous
find a formula for the area inside the cardoid r=a+acos(thetat), a>0
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
a cardoid is a circle with a little pinched thingy like a navel
anonymous
  • anonymous
No thats an annulus. A cardioid is given by that function. The best way to solve this would be to integrate by polar coordinates. Do you know how to do that?
anonymous
  • anonymous
\[\int\limits_{0}^{2\pi}\int\limits_{0}^{a + acos(\theta)}rdrd \theta\]

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anonymous
  • anonymous
Watch your language on this site, talking about annulus.
anonymous
  • anonymous
...what's the expression inside cos( ? Is it r = a + a * cos(theta * t)?
anonymous
  • anonymous
davismj, usually what you'd do to find the area inside a polar curve, r, is to do one integration. In standard form: \[\frac{1}{2} \int\limits \ r^2 d\theta\] from the area of a circular sector, with infinitesimally small angles.
anonymous
  • anonymous
Your integral is equivalent to mine.
anonymous
  • anonymous
Exactly, it's just that it seems like the OP's type of problem is usually solved with a simpler form of the integral. Just wanted to point it out, in case he/she hasn't seen multiple integrals yet.
anonymous
  • anonymous
Good point.

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