Answer
$\int_{-2}^2 (x^9 - 3x^5 + 2x^2 -10) dx = \frac{-88}{3}$
Work Step by Step
$\int_{-2}^2 (x^9 - 3x^5 + 2x^2 -10) dx = \int_{-2}^2 x^9 dx - \int_{-2}^2 3x^5 dx + \int_{-2}^2 2x^2 dx - \int_{-2}^2 10 dx$
Because $f(x) = x^9$ and $f(x) = -3x^5$ are odd functions and $f(x)=2x^2$ is an even function:
$= 0 + 0 + 2\int_0^2 2x^2 dx - \int_{-2}^2 10 dx = 4\int_0^2 x^2 dx - \int_{-2}^2 10dx = 4(\frac{1}{3}(2)^3) - (10(2) - 10(-2)) = \frac{32}{3} - 40 = \frac{-88}{3}$
