Answer
$\pi-2$
Work Step by Step
Let us consider that two continuous functions $f(x)$ and $g(x)$ with $f(x)\geq g(x)$ on the interval $[a,b]$ . The area (A) of the region bounded by the graph of $f(x)$ and $g(x)$ on the interval $[a,b]$ can be calculated as: $Area(A)=\int_a^b [f(x)-g(x)] \ dx$
Thus, the area of the region is:
$A=\int_a^b [f(x)-g(x)] \ dx= \int_{0}^{\pi/2} (2-2 \sin x) \ dx \\=[2x+2 \cos x]_0^{\pi/2}\\=[2(\dfrac{\pi}{2})+2\cos (\dfrac{\pi}{2})]-[0+2 \cos (0)] \\=\pi+0-0-2 \\=\pi-2$