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David.Butler

  • 2 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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  1. JamesJ
    • 2 years ago
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    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 \[ \int_0^{2\pi} \int_{r_2}^{r_1} r \ dr \ d\theta \]

  2. David.Butler
    • 2 years ago
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    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.

  3. JamesJ
    • 2 years ago
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    Ah, good. In which case, that's the range of values for theta.

  4. JamesJ
    • 2 years ago
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    Another good reason to draw the graph!

  5. zepdrix
    • 2 years ago
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    |dw:1359669259799:dw|Hmm I was trying to draw the graph :L it's pretty tricky though lol

  6. zepdrix
    • 2 years ago
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    |dw:1359669390955:dw|

  7. zepdrix
    • 2 years ago
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    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

  8. David.Butler
    • 2 years ago
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    Oh no your right! Thanks , I kept doing the problem wrong , I was using the wrong bounds! Thanks So much

  9. zepdrix
    • 2 years ago
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    Ah ok cool c:

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