differentiator is used in t.v.
phase shift in integrator is 180 degrees and phase shift in differentiator is 0 degrees
It doesn't. It can produce any waveform if you feed the integral of the desired waveform into the differentiator's input.
remote car
noise is a ac signal(high frequency range), as LPF allows only lower frequencies integrator is has more noise immunity than differentiator
Finding the rate of change - in particular, the instantaneous rate of change.
a phase shifted sine wave of a different amplitude.
A differentiator
Because the capacitor is in series with the output. Vice versa for the integrator.
A high pass circuit can act as a differentiator because it allows high frequency signals to pass through while attenuating low frequency signals. This property causes the output to respond more to the rate of change of the input signal, making it behave similar to a mathematical differentiator.
The op amp differentiator is generally not used in any analog computer application. The basic reason for this is that high-frequency noise signals will not be suppressed by this circuit; rather they will be amplified far beyond the amplification of the desired signal.
infinite positive impulse wave on each leading edge, infinite negative impulse wave on each trailing edge. the rest of the time it is 0V. this assumes an ideal square wave, which I must assume as you did not give rise/fall times or edge slew rates.