Finding the shared area of 2 polar equations

1. Dec 4, 2011

shortman12012

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. Dec 4, 2011

hunt_mat

To find the limits of the integral, equate the equations, so set:
$$5-3\cos\theta =5-2\sin\theta$$
This will give two values of theta for your limits.

3. Dec 4, 2011

shortman12012

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 ?

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook