Suggestion: There are several moments of inertia definitions and there are also moments of inertia calculated for basic geometric figures, and they are listed in tables. E.g. see reference:
Schaum's Outline Series "Theory and Problems of Engineering Mechanics," 3rd edition, by Mc Lean and Nelson (McGraw-Hill Book Company).
Chapter 16 Mass Moments of Inertia
Ix=integral of (y**2 + z**2)dm
Iy=
Iz=
Jo=integral of ro**2 dm = Ix+Iy
etc.......