Explanation:

When we integrate a signal, we are essentially summing the input over time. The integration frequency is the frequency at which the amplitude of the integrated output starts to roll off due to the capacitance in the circuit.

The formula for the integration frequency is given by:

Integration frequency = 1 / (2*pi*RC)

where R is the resistance in the circuit and C is the capacitance.

Explanation of the formula:

The integration frequency is the frequency at which the output voltage starts to roll off due to the capacitance in the circuit. This means that the output voltage decreases as the frequency of the input signal increases. The rate at which this decrease happens is determined by the time constant of the circuit, which is given by RC.

The time constant of the circuit is the time it takes for the output voltage to reach 63.2% of its final value. This means that if we apply a step input to the circuit, the output voltage will reach 63.2% of its final value after one time constant.

The formula for the time constant is given by:

Time constant = RC

Since the output voltage decreases as the frequency of the input signal increases, we can say that the integration frequency is the frequency at which the output voltage has decreased to 1/sqrt(2) or 0.707 of its original value. This occurs when the frequency of the input signal is equal to 1/(2*pi*RC).

Therefore, the integration frequency is given by:

Integration frequency = 1 / (2*pi*RC)

Conclusion:

The integration frequency is the frequency at which the amplitude of the integrated output starts to roll off due to the capacitance in the circuit. The formula for the integration frequency is given by 1 / (2*pi*RC), where R is the resistance in the circuit and C is the capacitance.