RC integrator circuit - can a high RC product really by approximately equal to Vin / R?
I think the book is alluding to something like this: -



Here we have a capacitor being charged from a square wave via a series resistor. It looks like a triangular waveform (i.e. what an integrator would produce with the same square wave) but if you allowed the capacitor a longer time to charge (i.e. slowed down the frequency of the square wave) you'd get a more obvious exponential charge/discharge waveform.

If Vout only changes a little bit (because the frequency is significantly higher or R or C increased significantly), then the waveform would look more like an integration function. See the three slightly exaggerated options below: -