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anonymous
 3 years 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
anonymous
 3 years 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
 3 years 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 \[ \int_0^{2\pi} \int_{r_2}^{r_1} r \ dr \ d\theta \]

anonymous
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.0Ah, good. In which case, that's the range of values for theta.

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

zepdrix
 3 years 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
 3 years 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

anonymous
 3 years 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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