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**DarrenM** Find the area for one loop of $\displaystyle r^{2} = 64sin2\theta$

I plotted three graphs; $\displaystyle r^{2}$ vs. [tex]\theta]/math], where it looks like a normal sin curve repeating twice between 0 and $\displaystyle 2\pi$ ranging from 64 to -64. Another of r vs. $\displaystyle \theta$ where it looks kind of like two elliptical shapes ranging from -8 to 8, restricted to 0 to $\displaystyle \frac{pi}{2}$ and $\displaystyle \pi$ to $\displaystyle \frac{3\pi}{2}$. Finally, the polar graph on x and y axis, where it looks like a lemniscate reaching a limit of 8 at $\displaystyle \frac{\pi}{4}$ and $\displaystyle \frac{5\pi}{4}$.

I did this:

$\displaystyle A=\int_{0}^{\frac{\pi}{2}} \frac{1}{2}(64sin2\theta) d\theta$