Example 23.3 analysis derivation assumes a uniform charge density for the entire disk surface area bounded by 0 and R. Suppose that we are interested with the E field contribution at P due to the charge density found between outer rim of dr and R. First draw that shows what it may look like graphically before diving into the analysis.

A uniformly charged disk of radius R. The electric eld at an axial point P is directed along the central axis, perpendicular to the plane of the disk