Answer
$3$
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:
$A=\int_a^b [f(x)-g(x)] \ dx\\ = \int_{2}^{3} [\dfrac{x}{2}-(3-x)] \ dx +\int_{3}^{6} [\dfrac{x}{2}-(x-3)] \ dx \\= \int_{2}^{3} [\dfrac{3x}{2}-3)] \ dx +\int_{3}^{6} [3-\dfrac{x}{2}] \ dx \\=[\dfrac{3x^2}{2}-3x]_2^3 +(3x-\dfrac{x^2}{4}]_3^6 \\=3$
