moment of inertia of continous mass systems can be calculated by integration.

 KEY STEPS-

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.