How do you know if an op amp on a circuit is working as low pass filter or as integrator?
There is not much difference between a low pass filter and an integrator. In its purest form, an op amp integrator has an input resistor connected from input to the negative input pin and a capacitor connected from the output back to the input. The plus input is grounded. It has infinite gain (limited by the open-loop gain) at DC. A simple op amp low pass filter will also have resistor in the feedback loop that sets a finite gain at DC and frequencies below the RC time constant. In the frequency region where the capacitor has a lower impedance than the feedback resistor, the two circuits will look the same. But an integrator will integrate up any DC signal (including the op amp offset) and eventually stop at the power supply level. There is usually a switch in parallel with the capacitor for reset.