Electrical – Find voltage across Resistor w/ Op Amp

Slew rate is the maximum dv/dt the op amp can produce at its output, and it doesn't depend on frequency.

This means that at high frequencies, the output will be distorted. The distortion happens when the slew rate is not enough to support the dv/dt required to accurately produce a sinusoidal output. Since the dv/dt of the sine wave depends on both the frequency and the amplitude, you can reduce the distortion by reducing either one.

Edit

what frequency should I use to measure my slew rate?

As you found, you can measure the slew rate at any frequency that is fast enough to exercise the slew rate limiting behavior. As discussed above, the minimum frequency to see the slew rate also depends on the input amplitude. You could also use a step input rather than a sinusoid to measure the slew rate.

a)

1. I think you missed a minus sign in (I_f) current equation , according to the current direction.

2. Don't know why you used dV_out = dQ/C and then again replaced dQ=dV_out*C. No effect.

3. Didn't understand what you tried to do line #4. you should just do an integration in line #3 with limiting value on Vout. e.g at t=0 Vout=0 and t=t Vout=Vout. Final equation is right though.

4. The waveforms are correct .

b) T=RC is time constant. It acts as a gain constant for the integrator. If you provide a square signal with period T, the RC value should be greater than or equal to T/2 to get a triangular waveform. Otherwise the capacitor won't get enough time to charge or discharge.