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**Diamondlance** I want to find the area inside $\displaystyle f=3+3\cos{\theta}$ and outside $\displaystyle g=3+3\sin{\theta}$ (we're in polar coordinates).

After making a sketch and finding the intersection points at $\displaystyle \theta=\frac{\pi}{4},\; \frac{5\pi}{4}$, I set up the integral

$\displaystyle \frac{1}{2}\int_{-3\pi/4}^{\pi/4}(f^2-g^2)\;d\theta$ thinking it would give me the area I want, and obtained $\displaystyle 18\sqrt{2}$.

However, the answer in the back of my textbook is $\displaystyle 9\sqrt{2}+\frac{27\pi}{8}+\frac{9}{4}$.

I checked the actual integration in Maple, so either the integral was set up incorrectly or the back of the textbook answer is wrong. I can't see what if anything I've done wrong, however I'm quite rusty at these types of problems so I wanted to ask if you see anything wrong with what I did. Thanks in advance.