Integrated Amp
if I have a sine wave through an integration of op-amp, then I get a signal that is 90 degrees out of phase and reversed?
since the integral of sinx =- cosx + C (back pressure on the ratings of capacitor)
Basically, yes. And here "but" ... The inverse of the time constant of R and C of the integrator must be much lower than the frequency of the sine wave - By at least a factor of 10 * 2pi. The highest 'away', you get the more accurate will be 90 degrees. The output will be attenuated input, also, then it should be amplified. An integrator is a lowpass filter. If you look at the phase Bode plot of a lowpass RC (1 pole) you'll notice that -90 degrees is fairly constant well beyond the cutoff frequency (this is where you operate as an integrator), but it * is * a filter, so there is a mitigation ..