Why would we transform an LC ladder filter to a integrator based active filter?? Is it simply because it gets 0 dB in the passband?
What's the advantage over just using LC ladder?
As the most important reason, the function of the inductance (coil) is replaced by an opamp.
Each wired inductor has unwanted properties: Heavy, EMC (radiation and sensitivity), no tuning capability, cannot be integrated, mechanically sensitive,...
More than that, active integrators provide a (low-resistive) voltage output, thus no additional buffer needed.
The active feedback is required to emulate the effect of inductors in the circuit and give higher values of Q (or damping factor) for higher order filters with sharper rolloff at the corner frequency then is possible with a passive network of only capacitors and resistors. Active filters are a way to get the good filter response of an LC filter without the L.
I must confess that I don`t understand this question.
No capacitor is "converted to active based".
As there are some different methods to convert passive LC into RC-active topologies (active L, FDNR technique, Leapfrog, FLF,...) , you should be more specific.
It`s best to show us a circuit you are referring to.