Let the radius of the thin circular disc be R and its mass be M which is rotating about an axis perpendicular to the plane of the disc and passing through the centre.

consider an element ring of radius r, thickness dr and mass dm.

dm= (M/π R²)2πr dr = (2M/R²)r dr

I= ∫r² dm = ∫r² (2M/R²)r dr

= (2M/R²)r⁴/4   ,( with limits 0 to R) = MR²/2

I= MR²/2