I have scanned the question I am working on and attached it as an image to this thread. A hint on this question would be good enough.
I have scanned the question I am working on and attached it as an image to this thread. A hint on this question would be good enough.
Note that $\displaystyle r=\cos\theta$ is a circle with center at $\displaystyle \left(\frac{1}{2},0)$ and radius $\displaystyle r=\frac{1}{2}$.
Similarly, $\displaystyle r=\sin\theta$ is a circle with center at $\displaystyle \left(0,\frac{1}{2})$ and radius $\displaystyle r=\frac{1}{2}$.
Now these circles will overlap at some point. So my hint is this:
When considering the region of intersection, split it up into two separate regions. Due to how we find limits of integration in polar coordinates, each region will be defined over different ranges for $\displaystyle \theta$. So your integrals will look something like:
$\displaystyle \displaystyle\int_{\theta_0}^{\theta_1} \int_0^{\cos\theta} r\,dr\,d\theta+\int_{\theta_0^{\prime}}^{\theta_1^ {\prime}}\int_0^{\sin\theta}r\,dr\,d\theta$
where $\displaystyle \theta_0\leq \theta\leq\theta_1$ is the range you consider for the $\displaystyle r=\cos\theta$ part, and $\displaystyle \theta_0^{\prime}\leq \theta\leq\theta_1^{\prime}$ is the range you consider for the $\displaystyle r=\sin\theta$ part.
Can you proceed? If you still have issues, post back!