A practical integrator is called a "lossy integrator" because of the presence of input resistance (Rin) in parallel with the feedback capacitor (Cf).
Key reasons for the name "lossy":
1. The parallel combination of Rin and Cf creates a lossy path that allows some signal energy to bypass the capacitor
2. At high frequencies, the signal can flow through Rin, resulting in signal loss
3. The integrator action is frequency-dependent - it provides perfect integration only at very specific frequency ranges
4. Below a certain cutoff frequency (determined by Rin and Cf), the circuit behaves more like an inverting amplifier than a true integrator
5. The impedance of Rin allows charge to leak from the capacitor, hence the term "lossy"
In an ideal (lossless) integrator, only a capacitor would be used in the feedback path, with infinite input resistance. The practical integrator sacrifices ideal behavior for stability and realistic performance.