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- anonymous

Area between two polar curves?
Find the area inside the circle r = 3*a*cosx and outside the cardiod r = a*cosx + a, where a > 0

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- anonymous

- chestercat

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- JamesJ

So always start with a diagram: I'll let you draw that. It's not too bad.
Call the first function r1. That is r1 = 3a.cos(theta) , and I assume by the way you meant to write theta, not x? And the second function r2.
Then the area is the integral
\[ \int_0^{2\pi} \int_{r_2}^{r_1} r \ dr \ d\theta \]

- anonymous

Why are the bounds for the second integral 0 to 2pi ? They intersect at pi/3 and 5pi/3.
Thanks , I truly appreciate the help.

- JamesJ

Ah, good. In which case, that's the range of values for theta.

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- JamesJ

Another good reason to draw the graph!

- zepdrix

|dw:1359669259799:dw|Hmm I was trying to draw the graph :L it's pretty tricky though lol

- zepdrix

|dw:1359669390955:dw|

- zepdrix

The circle is drawn by the `outer` radius, so we subtract the inner radius from the outer.\[\large \int\limits_{-\pi/3}^{\pi/3} 3a \cos x-(a \cos x+a) \quad dx\]
Is the lower limit 5pi/3? I think it's -pi/3.
a>0.. Hmm maybe not.
Grr now I'm confusing myself :) lol

- anonymous

Oh no your right! Thanks , I kept doing the problem wrong , I was using the wrong bounds!
Thanks So much

- zepdrix

Ah ok cool c:

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