Answer
$\dfrac{81}{2}$
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:
$A=\int_a^b [f(x)-g(x)] \ dx= \int_{-3}^{0} (x^3-9x) \ dx+\int_{0}^{3} (9x-x^3) \ dx \\=[\dfrac{x^4}{4}-\dfrac{9x^2}{2}]_{-3}^{0}+[\dfrac{9x^2}{2}-\dfrac{x^4}{4}]_0^3 \\=[0-(\dfrac{81}{4}-\dfrac{81}{2})]+[\dfrac{81}{2}-\dfrac{81}{4}]-0\\=\dfrac{81}{2}$
