SO we need the area inside one petal, the formula we need is

SO in order to do that we need the theta values where our function equals zero. 0=sin2theta. We take the first two values which are 0,pi

so then we find

A=int 1/2(sin^2(2theta))dtheta from 0 to pi

That becomes

A=1/16 (4 theta-sin(4 theta)) from 0 to pi, which equals pi/4
So your answer is E.

Apr 28th, 2015

Now, I am reading that theta restriction as limiting our function to the first quadrant, but we could evaluate from 0 to pi/2 and get pi/8. Can you tell me if this is a restriction or theta value based on previous problems? It can be read both ways