Finding the shared area of 2 polar equations

  • #1

Homework Statement



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


Homework Equations



A= 1/2∫ r^2 dθ

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.
 

Answers and Replies

  • #2
hunt_mat
Homework Helper
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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.
 
  • #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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