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Cardoid area

  • Thread starter rcmango
  • Start date
  • #1
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Homework Statement



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

Homework Equations



r = 6·cosθ
r = 2 + 2·cosθ

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
 

Answers and Replies

  • #2
dextercioby
Science Advisor
Homework Helper
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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.
 
  • #3
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heres what i got so far.. can u please help finish this problem.

heres where i'm at: http://img109.imageshack.us/img109/4070/untitledxz9.jpg [Broken]
 
Last edited by a moderator:
  • #4
HallsofIvy
Science Advisor
Homework Helper
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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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