The output voltage as function of time is given by the next formula in the integration circuit.
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Formula 1
Where:
Vout is the output voltage in volts (V)
Vin is the input voltage in volts (V)
R is the resistance in ohm (Ω)
C é the capacitance in farads (F)
Vin and Vout are really functions that describe the input and output voltages.