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Parametric Equation intersection and area

  1. Jun 9, 2012 #1
    1. The problem statement, all variables and given/known data
    Given the curves r=2sin(θ) and r=2sin(2θ), 0 ≤ θ ≤ pi/2, find the area of the region outside the first curve and inside the second curve


    2. Relevant equations
    obviously set up an intersection to see where the two meet, then subtract the circle equation from the rose equation.


    3. The attempt at a solution

    First setting up the intersection:
    2sin(θ) = 2sin(2θ)
    sin(θ) = sin(2θ)
    sin(θ) = 2sin(θ)cos(θ)
    1 = 2cos(θ)
    1/2 = cos(θ)
    pi/3 = θ

    so then setting up the integrals, you have sin(θ) dθ bound by pi/3 to pi/2 minus 2sin(2θ) dθ bound by pi/3 to pi/2

    working through it, I was able to get an answer of 1/2, but entering it in, the answer turned out to be incorrect. Any help here would be greatly appreciated, thank you.
     
  2. jcsd
  3. Jun 9, 2012 #2
    Hi BradyK! Welcome to PF!! :smile:

    You should recheck those limits. You are looking for the area outside the first curve r=2sin(θ) and inside the second curve r=2sin(2θ).
     
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