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Finding the shared area of 2 polar equations

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data

    Given the two polar equations r=5-3cos(θ) and r=5-2sin(θ) find the area of the region common to both curves.


    2. Relevant equations

    A= 1/2∫ r^2 dθ

    3. The attempt at a solution
    i understand that i plug in the two equations into the equation, but i dont know how to find the limits of integration.
     
  2. jcsd
  3. Dec 4, 2011 #2

    hunt_mat

    User Avatar
    Homework Helper

    To find the limits of the integral, equate the equations, so set:
    [tex]
    5-3\cos\theta =5-2\sin\theta
    [/tex]
    This will give two values of theta for your limits.
     
  4. Dec 4, 2011 #3
    correction it should be 5-3cosθ =5-3sinθ, but after equating those two and solving i got
    θ=π/4,5π/4
    so now would the correct integral for solving the shared area of the two limaçon
    A = ∫(5−3cos(θ))^2 dθ + ∫(5−2sin(θ))^2 dθ ?
     
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