Problem # 43

Moment of Inertia, Rigid Body
The mass moment of inertia of a slender rod of length L and mass m is given by the equation :

for the rotation about the axis perpendicular to this paper through its center of mass, G, which is located halfway between its two end points.

Derive this equation using the definition of the central mass moment of inertia :
where "r" is the distance of a mass-element "dm" from the center of mass of the rod. Please, define carefully your "dm" and whatever variables you are using.