$($a$)$ Derive the transfer function for an integrator circuit and plot

the gain frequency response.

$($b$)$ Determine the transfer function and draw the pole$-$zero plot of

the circuit of Fig$\mathrm{.}3.$

$($c$)$ Design a low pass active filter using suitable components to

achieve a unity gain frequency of $10$ kHz with a dc gain of $20$ dB and an input resistance of at least $10k$

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