Find the area of the region inside the inner loop of the limacon r=5-10cos(theta). I just need help setting it up!!

Question

miracrown · Answer

Let me post the graph for this function before we begin.

smurfy14 · Answer

Ok! What I'm struggling with is: I have no idea how to find the endpoints of the integral.

miracrown · Answer

The region of interest to us in this problem is the inner lobe, which I highlighted in yellow: http://screencast.com/t/YZR7pwB3u

miracrown · Answer

Ok - that is the key (and tricky) part to this problem. 
The inner lobe of the limacon starts and ends when r = 0.
Let me mark this point (which is the origin) in red.

miracrown · Answer

http://screencast.com/t/LBp51GxQsK

miracrown · Answer

let's now find the theta values that result in r = 0.

miracrown · Answer

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