Find the area inside the larger loop and outside the smaller loop of the limacon

r= 1/2 + Cos[x]

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- Jul 21st 2007, 04:28 PMcamherokidPolar Coordinate..
Find the area inside the larger loop and outside the smaller loop of the limacon

r= 1/2 + Cos[x] - Jul 21st 2007, 04:52 PMgalactus
The region between the loops would be:

- Jul 21st 2007, 04:58 PMJhevon
- Jul 21st 2007, 05:52 PMcurvature
the graph

- Jul 21st 2007, 05:58 PMcamherokid
so what is the answer right?

- Jul 21st 2007, 06:02 PMJhevon
I never calculated the answer, I assume you are capable of doing the integration on your own, so I don't know what answer you got or whether or not it is correct.

I do believe galactus' solution would give a different answer from mine though, but i think i'm right (i may be wrong :D)

i'd go with the first formula i used, not the difference of two integrals, but the single one - Jul 21st 2007, 06:09 PMcurvature
- Jul 21st 2007, 06:12 PMJhevon
- Jul 21st 2007, 06:18 PMcurvature
- Jul 21st 2007, 06:31 PMcurvature
- Jul 21st 2007, 06:35 PMcurvature
- Jul 22nd 2007, 06:38 AMSoroban
I agree with Galactus . . .

Quote:

Originally Posted by**galactus**

I would use: .

The integral is: .

. .

The "outer" area is: .

. .

. .

The "inner" area is: .

. .

. .

The desired area is: .

Check my work . . .*please!*

I've check and double-checked.

. . If there are errors, I can't find them.

- Jul 22nd 2007, 07:26 AMgalactus
That's what I got, Soroban.