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Cardoid area

  1. Feb 14, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the area of the region that is inside the circle r = 6cos(theta) but outside the cardoid r = 2 + 2cos(theta)

    2. Relevant equations

    r = 6·cosθ
    r = 2 + 2·cosθ

    3. The attempt at a solution

    intersections of the two curves.

    6·cosθ = 2 + 2·cosθ → 4·cosθ = 2

    cosθ = 1/2 → θ = ±π/3

    Can someone finish the integral for me, i'm not good at integrals, this is as far as i can get. thanks for any help.

    A = 2 x (1/2) ∫ [(6·cosθ)² - (2 + 2·cosθ)²] dθ
  2. jcsd
  3. Feb 14, 2007 #2


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    Homework Helper

    You still need a picture. Use math software and ask it to draw both graphs in polar coordinates (they should be [itex] \left(\rho,\varphi\right) [/itex], not "r" and "theta") and just then you can set up a correct integral.
  4. Feb 15, 2007 #3
  5. Feb 16, 2007 #4


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    Staff Emeritus
    Science Advisor

    No, I will not do the integral for you. I will give you a hint: to integrate [itex]cos^2(\theta)[/itex], use the trig identity [itex]cos^2(\theta)= \frac{1}{2}(cos(2\theta)+ 1).
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