Determine tensor of inertia of a rod

[Like Tony Stark]

Homework Statement

The pictures show two rods of homogeneous mass ##m## and length ##l##. Determine their inertia tensors.

Relevant Equations

Matrix of inertia

I have to find the inertia tensor of these rods and I don't have the concept that clear...
I mean, I know the formulas like:
##I_{xx}=\int y^2 + z^2 dm##
##I_{xy}=\int xy dm##

But I don't know what ##x, y, z, dm## stand for. In other words, I don't know what I should replace in the formula with.

Can you do one example for me? Just one, like "in the first picture, if you want to calculate ##I_x##, where you have ##y## you have to replace with b because that's..., and where you have ##z## you have to replace with 0 because..."

And what would it be the difference if these pictures didn't show rods but cylinders or another shape?

Thanks

 

[haruspex]

The general principle is that dm is a mass element at some (x,y,z), so if the density there is ##\rho## then ##dm=\rho dxdydz##. Substituting that gives you a triple integral for each tensor component,
Given that this is just a rod, it will probably be more convenient to introduce ds as a length element and use a mass per unit length density. Expressing the coordinates as functions of s should give you single integrals.