Answer
$ \dfrac{\pi}{2}$
Work Step by Step
Our aim is to integrate the integral and find the area using polar coordinates as follows:
$ Area=\int^{3\pi/4}_{\pi/4} \int^{2 \sin\theta}_{ \csc\theta} \space r \space dr \space d\theta $
or, $=\dfrac{1}{2}\int^{3\pi/4}_{\pi/4}(4 \sin^2\theta- \csc^2\theta) d\theta $
or, $=\dfrac{1}{2}[2\theta- \sin2\theta+ \cot\theta]^{3\\pi/4}_{\pi/4}$
So, $ Area= \dfrac{\pi}{2}$
