Answer
$128$
Work Step by Step
$\int_0^4 6x - x^3 + 10xdx$
$= [3x^2 - \frac{1}{4}x^4 + 5x^2]_0^4$
$48 - 64 + 80 = 64$
Since the graph is symmetric, we can just multiply our answer by 2 for the other half.
$64 * 2 = 128$
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