In Figure (a), if R2 is replaced by a capacitor (having transformed impedance 1/sC) one get the circuit of Figure (a) which is an inverting integrator.
Figure: (a) Inverting Integrator (Miller Integrator); and (b) Inverting Differentiator
Replacing R2 in Eq. (7.55) by 1/ sC, the transfer function of the integrator of
Figure (a) is found to be
V 0 (S ) =- (1 / sC R 1 ) V (S )
or in time domain,
V0 (t ) =- 1 /C R1 ∫ V2 (t ) dt
which represents an inverting integrator.