What is the net area between f(x) = x-cosx  and the x-axis over x in [0, 3pi ]?

${\int}_{0}^{3} \pi \left(x - \cos\right) \mathrm{dx} = \left({x}^{2} / 2 - \sin x\right) {|}_{0}^{3 \pi}$
${\left(3 \pi\right)}^{2} / 2$
Note the $\sin 3 \pi$ evaluated at $0 \mathmr{and} 3 \pi$ is zero
insignificant the $\sin$ function adds a maximum of 1 and minimum of 0,so for large number the effect of $\sin x$ is insignificant and this integral approaches ${x}^{2} / 2$