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Finding area between two curves Polar Coordinates

  1. Sep 7, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the area inside the circle r = 3sinθ and outside the carotid r = 1 + sinθ




    3. The attempt at a solution
    Alright so I graphed it and found that they intersect at ∏/6 and 5∏/6.
    I can't think of a good way to approach the problem. The carotid has some of it's area beneath the x-axis otherwise I would take the area of the 3sinθ - the area of the other one. Will it work if set the limits of integration to pi/6 and 5pi/6 and take the integral of (3sinθ - (1+sinθ)? I'm a bit lost
     
  2. jcsd
  3. Sep 8, 2013 #2

    Zondrina

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    Yes, that all seems reasonable. Just compute your integral and you're done.
     
  4. Sep 8, 2013 #3
    I got 1.369705. Is there any online integral doer I can use to check my work?
     
  5. Sep 8, 2013 #4

    Zondrina

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    Yes, that's the correct answer. Wolfram alpha is good for checking your work afterwards.
     
  6. Sep 8, 2013 #5

    LCKurtz

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    Gold Member

    NO. That's the wrong integrand. Look up the formula for polar area.
     
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