Take the graph infinitesimal, and the infinitesimal area dS=rdrdθ.
Infinitely small mass dm=(m/πR? )dS=(m/πR? )rdrdθ
Moment of inertia of disk J=∫∫dmr? =(m/πR? )∫∫r? drdθ=(m/πR? )∫dθ∫r? Doctor?
Substitution? θ integration interval 0-2 π,,, r integration interval 0-r integration can be obtained:
J=mR? /2