Hi. Looks like it's:
Consult this picture: http://i43.tinypic.com/f224xz.jpg
I want to find the area of the region enclosed by the green outline (so basically the whole yellow/opaque yellow region)
The bigger curve is r=2cos(2theta+(pi/2)) and the smaller curve is just r=cos(2theta)
I thought it would be easiest to find the area of the blue region or the red region and then multiply by 8 and do some subtraction, etc. to get the area I want.
However, I am not sure what to integrate because the theta values of intersection of the curves are different for each curve.
How do I do it?
as can be seen in that graph, for the bigger 4-petal-rose, those limits would work. If i was just trying to find the area of the bigger rose, I could take 1/2 the integral from 0 to pi/2 and multiply my result by 4. Correct?
and then for my total area I am seeking (both curves), just add on the 8 * [the first integral in your equation from 0 to .2318..]
hmm EDIT: i think I am seeing what your doing now. you arent getting the full areas of curves, but rather the area up to a diagonal line that is shared in both integrals.