Answer
$$A = \frac{{256}}{5}$$
Work Step by Step
$$\eqalign{
& \left( i \right){\text{From the graph we can see that the net area of the region is:}} \cr
& A = \int_{ - 2}^2 {\left( {16 - {x^4}} \right)} dx \cr
& {\text{Integrating}} \cr
& A = \left[ {16x - \frac{1}{5}{x^5}} \right]_{ - 2}^2 \cr
& {\text{Evaluating}} \cr
& A = \left[ {16\left( 2 \right) - \frac{1}{5}{{\left( 2 \right)}^5}} \right] - \left[ {16\left( { - 2} \right) - \frac{1}{5}{{\left( { - 2} \right)}^5}} \right] \cr
& A = \frac{{128}}{5} + \frac{{128}}{5} \cr
& A = \frac{{256}}{5} \cr} $$
