Chapter 5.6, Problem 353E

Consider the solid enclosed by the cylinder $x^2-z^2=a^2$ and the planes $y=b$and $y=c$. where $a>0$ and b < c are real numbers. The density of Q is given by $\rho \left(x,y,z\right)=f\text{'}\left(y\right)$. where f is a differential function whose derivative is continuous on (b, c). Show that if f(b) = f(c). then the moment of inertia about the xz-plane of Q is null.