## Calculus: Early Transcendentals 8th Edition

$\int_{-\pi/3}^{\pi/3}x^4~sin~x~dx = 0$
The function $~~f(x) = sin~x~~$ is an odd function while $~~g(x) = x^4~~$ is an even function. Then $~~x^4~sin~x~~$ is an odd function. Therefore: $\int_{-\pi/3}^{\pi/3}x^4~sin~x~dx = 0$