Differences between Active/passive integrator/differentiators

[mathman44]

Homework Statement

Hi,

I have a few questions about some differences between the two.

Why does an active integrator circuit, using an op-amp, not have the frequency restrictions found in a passive integrator circuit? Why does this also apply for two type of differentiator circuits?

Lastly, can active integrators/differentiators be used as low-pass and high-pass filters, respectively, in the same way as their passive circuit counterparts?

 

[mmmboh]

The first one has to do with the fact that the output of a passive integrator circuit only integrates the signal if Vo<<Vi, so R>>1/wc.