Answer
$\dfrac{9}{4}$
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:
$A=\int_a^b [f(x)-g(x)] \ dx\\ = \int_{-\pi/6}^{\pi/6} [\cos y -(-\sin 2y)] \ dy \\=[\sin y -\dfrac{\cos 2y}{2}]_{-\pi/6}^{\pi/6}\\=\dfrac{3}{2}-(\dfrac{1}{2})(-\dfrac{3}{2}) \\=\dfrac{9}{4}$
