Solution
= Solution
Here $a=0$, so the <probability density function> is the <even function> $\cos x$ on $[-h,h]$, where $h=\pi/6$. Hence $\mathbb E[X]=0$ by <odd function>[oddness], and the <variance> is just $\mathbb E[X^2]$. Two applications of <integration by parts> give
$$
\int x^2\cos x\,dx=x^2\sin x+2x\cos x-2\sin x+C.
$$
Thus
$$
\operatorname{Var}(X)=2\left[h^2\sin h+2h\cos h-2\sin h\right]=\boxed{\frac{\pi^2}{36}+\frac{\pi\sqrt3}{3}-2}.
$$