What are differentiator and integrator circuits using op-amps?

An integrator uses a capacitor in the feedback path and resistor at input, producing an output proportional to the integral of the input signal over time (Vout = -1/RC * integral of Vin). A differentiator uses a capacitor at input and resistor in feedback, producing output proportional to the rate of change of input (Vout = -RC * dVin/dt). Both are fundamental in analog computing and signal processing.