if I have a sine wave thru an integrating op-amp, do I get a signal that is 90degrees off phase and inverted?

Question

since the integral of sin x = -cosx + C (previous voltage on feedback capacitor)

Answer 1

Basically, yes.

Here's the "but"... The inverse of the time constant of the R and C of the integrator has to be much less than the frequency of the sine wave -- by at least a factor of 10*2pi. The further 'away' you get the more accurate the 90 degrees will be.

The output will be attenuated from the input, too, so it will have to be amplified.

An integrator is a low-pass filter. If you look at the Bode phase plot of an RC low pass filter (1 pole), you'll notice that the -90 degrees is pretty constant well past the cutoff frequency (this is where you operate it as an integrator), but it *is* a filter, so there is attenuation.

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