During the steady-state condition of a differentiator, the average output voltage is zero volts.

If the output of an RC integrator is zero volts, the capacitor might be open.

The output of an RC differentiator is taken from across the capacitor.

The output of a differentiator could be considered a spike when the input pulse width is much longer than 5 time constants.

The output voltage of an RC integrator will eventually equal the voltage of a single input pulse if the input pulse width is less than 5 time constants.