The integrator circuit does exactly what you would think that it does...it takes the input voltage and integrates it to give the output voltage. Yes, circuits can do calculus.

This video derives the equation for the relationship between input and output voltage of an integrator circuit, provides some examples of where you might find such a circuit, and goes through a few simulation examples.

To see other common operational amplifier configurations check out:
https://www.electronx.ca/education/op...

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