Q.Sketch the output of an integrator if the input is a sine wave.

An op-amp integrator produces an output proportional to the time integral of its input. It is built like an inverting amplifier but with the feedback resistor replaced by a capacitor $C$: the input $V_i$ reaches the inverting $(-)$ node through an input resistor $R_i$, the feedback element is capacitor $C$, and the $(+)$ terminal is grounded.

Using the virtual ground, the input current $V_i/R_i$ flows into the feedback capacitor and charges it. Since a capacitor's voltage is the integral of the current through it, the output is

The negative sign shows the integrator also inverts. The output at any instant represents the accumulated area under the input waveform, scaled by the time constant $R_i C$.

The characteristic waveform transformations make the action easy to recognise: …