moment of inertia of continous mass systems can be calculated by integration.
1.write dm of a small element which is at a distance dx from the axis of rotation.
2.use I = integral of r2dm
over the entire length,area or volume respectively as you have chosen linear mass density (
) , surface mass density (
) , volume mass density (
) for writing dm.
3.remember standard formulas for ring disc cone hollow and solid sphere etc. and use it for writing dI and integrate.