Answer
$$0$$
Work Step by Step
$$\eqalign{
& \int_{ - 200}^{200} {2{x^5}dx} \cr
& {\text{testing for symmetry}} \cr
& f\left( x \right) = 2{x^5} \cr
& f\left( { - x} \right) = 2{\left( { - x} \right)^5} \cr
& f\left( { - x} \right) = - 2{x^5} \cr
& f\left( { - x} \right) = - f\left( x \right){\text{ so the function }}2{x^5}{\text{ is odd}} \cr
& {\text{Use the theorem 5}}{\text{.4}} \cr
& {\text{If }}f\left( x \right){\text{ is odd}}{\text{, }}\int_{ - a}^a {f\left( x \right)dx} = 0 \cr
& then \cr
& \int_{ - 2}^2 {{x^9}dx} = 0 \cr} $$
