Final answer:
An OPAMP-based first-order lowpass filter acts as an integrator by allowing low-frequency signals to pass and attenuating high-frequency signals, aligning with the definition of an integrator. Conversely, a highpass filter, which passes high frequencies and blocks low frequencies, does not serve as an integrator. The components' behavior would switch if capacitors were replaced with inductors.
Step-by-step explanation:
An OPAMP-based first-order lowpass filter acts as an integrator in the scenario identified as (c) Integrator. This is because an integrator circuit is essentially a lowpass filter with a frequency response that decreases linearly with frequency, allowing it to integrate the input signal over time. A lowpass filter allows signals with a frequency lower than its cutoff frequency to pass through while attenuating higher frequencies. This is why the capacitor acts as a low-frequency filter, impeding the transmission of high-frequency signals, making it suitable for integration purposes.In contrast, scenario (b) refers to a Highpass filter, which would not act as an integrator because it passes high-frequency signals and attenuates those lower than its cutoff frequency. This means it does not accumulate signal values over time like an integrator does. If the capacitors in a filter circuit are replaced by inductors, the roles would reverse; inductors would act as high-frequency filters and capacitors as low-frequency filters. This is due to the inductive and capacitive reactance properties, which are frequency-dependent.