a detailed answer required. can inductors also be used or is there some drawback associated with them
Yes, inductors could also be used. For instance an inductor can perform integration: I (1/L)integral(V dt); as well as differentiation: V L di/dt . I'm thinking that there are maybe two reasons why we use RC integrators and differentiators instead of RL. This is my opinion only but it's based on many years of experience. First is that capacitors of a very wide range of values are easily obtained. Not so for inductors. If you're an electronics hobbyist or even an engineering lab for a large company, you will have lots more capacitors in stock than inductors. This has been true anywhere that I've ever worked. The right value capacitor is easy to get compared to the right value inductor. Second (and probably less important than the first reason) is that in many active integrator/differentiator circuits, it may be desirable to isolate the DC operating voltage of one stage from another, especially when operating from a single supply. Can't do this with an inductor. Other than that, I don't know. I guess that's just the way it is.
I am not sure you are asking you question right. A time constant of 1 nanosecond implies you are talking about frequencies in the100's Megahertz range. As you have seen the capacitor values are 1 picofarad, 0.1 picofarad, and 0.01 picofarad. I have never seen capacitors so small. Needless to say with these extremely small capacitance, capacitor lead length will add an appreciably amount to the capacitance.
