integrator opamp , differential opamp , adder opamp

dear everybody
could you pls tell me applications of the integretot , differential , adder opamp. i study all of them but i can not know what exactly their applications and features the difference
many thank in advance

Integrators can be one type of Low Pass Filter. They are used by some ADC or in wave shaping.
An integrator circuit produces a steadily changing output voltage for a constant input voltage.

Similarly, the Differentiators are High Pass filters.
A differentiator circuit produces a constant output voltage for a steadily changing input voltage.

Adders are used by some temperature, pressure or some other parameter measuring device and getting their average. Mathematical circuits.
If the input resistances of a summing amplifier are connected to potentiometers the individual input signals can be mixed together by varying amounts. For example, measuring temperature, you could add a negative offset voltage to make the display read "0" at the freezing point or produce an audio mixer for adding or mixing together individual waveforms (sounds) from different source channels (vocals, instruments, etc) before sending them combined to an audio amplifier.

Hi dinosaur !
And integrator can be used in many applications . for example converting an square wave to a triangle wave ( in SMPS or class D amplifiers or .... etc ) or perhaps as a funny wave shaper ! ( if you give a triangular wave to the input of an integrator you'll get something like a sine wave , but it is not pure ! ) and a differentiator can be used in a zero crossing detector or in a trigger system for power elements like triac or thyristors . or many other applications . also those circuits can be used as a filter ( HPF or LPF ) . and in an analog computer , of course ! and an adder amplifier : it can be used in current limiting systems . or it can be used as a mixer in audio systems . or an amplitude meters for amplifiers . or in analog computers . or in feedback loops to add an special function . or shifting a signal ( with a DC component ) . or many other applications .
Best Wishes
Goldsmith

Integration is used in low cost ADC that have the advantage of averaging the input with noise. look for "Integrate & Dump" type ADC for examples

Accelerometers with true piezo-electric type use charge amplifiers to produce a voltage that changes with acceleration, A and vibration. Since we know Velocity, V is the Integral of "A" and Position is the 2nd integral of A. Before digital computing became cheap, Integration was an obvious way to produce a velocity and position signal.

Many, many other present day sensors in industry, medical and scientific applications also require integration to accumulate results over time and improve on sensitivity.

Here is a great article about op-amps, including integrator, differentiator, and summing circuits: https://www.allaboutcircuits.com/vol_3/chpt_8/1.html

Jump pages with the links on the left. It is clear, concise, and well-written, and mentions some possible applications for the different circuits as well.