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

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

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

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

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2The 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

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