Analog integration and differentiation:

a$)$ Predict the time dependence of $\backslash ($ V$\_\{\backslash$text $\{$out $\}\}\backslash )$ for the analog integrator op$-$amp with a resistor value of $\backslash (20\backslash$mathrm$\{$k$\}\backslash$Omega $\backslash )$ and capacitor value of $\backslash (100\backslash$mu $\backslash$mathrm$\{$~F$\}\backslash )$ for each of the input signals at $\backslash ($ V$\_\{$i n$\}\backslash )($square$,$ triangle, and sine$)$ shown below. Graph each function and give an explicit formula $($for one cycle$),$ including numbers $($based on measured input signal voltages and values of $\backslash ($ R $\backslash )$ and $\backslash ($ C $\backslash )).$

You may have built $($or may be building$)$ these $($or similar$)$ circuits in the lab. How do you expect your measured $\backslash ($ V$\_\{\backslash$text $\{$out $\}\}\backslash )$ signals will to compare to your predictions above $($including voltage levels$)?($Can you explain some possible discrepancies and the reasons for them$)?$

b$)$ Repeat the above for the analog differentiator. Is there one input signal that is more problematic than the others? If so$,$ which one, and why? What do you think will happen in real life?