Find the area bounded by the following polar curves $r<3|sin(2t)|$
Well, I know that the formula used to calculate an area bounded by $g(t) \le r \le f(t)$ with $\alpha \le t \le \beta$ is $A=\frac{1}{2} \int_{\alpha}^{\beta} [f(t)]^2 - [g(t)]^2 \,dt$
So, $g(t)=-3sin(2t)$ and $f(t)=3sin(2t)$. And then I have to look for the intersections between $g(t)$ and $f(t)$ to find $\alpha$ and $\beta$. And after that? Because they intersect each other in more than one interval. And also, how can I find the intersection? Because I have problems with the $(2t)$ of $sin(2t)$.
You'll see your error is you simply plot the curve:
$$A = 4 \int\limits_{\theta = 0}^{\pi/2} \int\limits_{r=0}^{|\sin (2 \theta)|} r\ dr\ d\theta = \frac{\pi}{8}$$