Can anyone help me with this problem?

Find the area shaded by the cardiods r=2+2cos(x) and r=2-2cos(x).

Thanks!

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- Jan 5th 2009, 09:59 PM #1

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- Jan 5th 2009, 10:04 PM #2

- Jan 5th 2009, 10:09 PM #3

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- Jan 6th 2009, 03:28 AM #4
Start by drawing sketch graphs of each cardioid. Calculate the polar coordinates of where they intersect. Then read this: Pauls Online Notes : Calculus II - Area with Polar Coordinates

- Jan 6th 2009, 03:54 AM #5

- Jan 6th 2009, 12:06 PM #6

- Jan 6th 2009, 06:19 PM #7

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I finally figured it out! Galactus, you were close, and I actually didn't quite get it until I saw your integral, but the equation should read:

$\displaystyle \int_{0}^{\frac{\pi}{2}}\left[2+2cos({\theta})\right]^{2}-\left[2-2cos({\theta})\right]^{2}d{\theta}=16$

Thanks for all your help, everyone!

- Jan 7th 2009, 03:34 AM #8
I started out with that, but then noticed 4 way symmetry. If I am wrong, then Soroban is wrong as well. I am not so sure we are wrong.

I also checked this with tech and got the same as Soroban and I. Therefore, I am going with our solution. Even thought the solutions are close.

S.O.S. Mathematics CyberBoard :: View topic - cardiods

- Jan 7th 2009, 04:37 AM #9