find the total area enclosed by a limacon r=1 +2cosTheta, use a double integral and symmetry

Question

blockcolder · Answer

The limacon is symmetrical about the polar axis. Thus, the area is 
$$2\int\limits_{0}^{pi}\int\limits_{0}^{1+\cos \theta}r dr d \theta$$.

anonymous · Answer

how did you set that up? :(

blockcolder · Answer

The area inside the limacon and above the polar axis can be described as {(r,theta)|0<=theta<=pi, 0<=r<=1+2cos(theta)}. Thus, the limits on r are 0 and 1+2cos(theta) and the limits on theta are 0 and pi.

anonymous · Answer

what.. is a limacon? :(

blockcolder · Answer

The first graph is the graph of a limacon. :D http://www.wolframalpha.com/input/?i=r%3D1%2B2cos%28theta%29

anonymous · Answer

what... the... freak. i've never even seen this! how am i supposed to know how to set this up? my professor is crazy.

blockcolder · Answer

Probably. =))

anonymous · Answer

thank you for your help!!

anonymous · Answer

oh i forgot to ask lol.. is the answer pi/2 ?