A slender metal arch, denser at the bottom than top, lies along the semicircle $y^2 + z^2 = 1$, $z \ge 0$, in the yz-plane (see the figure on the right).
Find $I_x$ if the density at the point $(x, y, z)$ on the arch is $\delta(x, y, z) = 5 - z$.
$I_x = $ (Type an exact answer.)