Answer
$\sqrt 3-\dfrac{\pi}{3}$
Work Step by Step
The area of the rectangle curve is=$(1/2)[5\pi/6-\pi/6]=\pi/3$
We need to find the area of the rectangle curve with limits $\pi/6$ to $5\pi/6$.
$A=\int_{\pi/6}^{5\pi/6} \sin x dx$
This implies that
$[-\cos x]_{\pi/6}^{5\pi/6}=[-\cos (5\pi/6)-(-\cos (\pi/6)]$
or, $-(\dfrac{-\sqrt 3}{2})+\dfrac{\sqrt 3}{2}=\sqrt 3$
Thus, the area of shaded region is: $\sqrt 3-\dfrac{\pi}{3}$
