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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
 one year ago
 one year ago
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
 one year ago
 one year ago

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JamesJBest ResponseYou've already chosen the best response.0
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 \[ \int_0^{2\pi} \int_{r_2}^{r_1} r \ dr \ d\theta \]
 one year ago

David.ButlerBest ResponseYou've already chosen the best response.0
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.
 one year ago

JamesJBest ResponseYou've already chosen the best response.0
Ah, good. In which case, that's the range of values for theta.
 one year ago

JamesJBest ResponseYou've already chosen the best response.0
Another good reason to draw the graph!
 one year ago

zepdrixBest ResponseYou've already chosen the best response.2
dw:1359669259799:dwHmm I was trying to draw the graph :L it's pretty tricky though lol
 one year ago

zepdrixBest ResponseYou've already chosen the best response.2
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
 one year ago

David.ButlerBest ResponseYou've already chosen the best response.0
Oh no your right! Thanks , I kept doing the problem wrong , I was using the wrong bounds! Thanks So much
 one year ago
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