We present a population study of the star formation history of 1244 Type 2 AGN host galaxies, compared to 6107 inactive galaxies. A Bayesian method is used to determine individual galaxy star formation histories, which are then collated to visualise the distribution for quenching and quenched galaxies within each population. We find evidence for some of the Type 2 AGN host galaxies having undergone a rapid drop in their star formation rate within the last 2 Gyr. AGN feedback is therefore important at least for this population of galaxies. This result is not seen for the quenching and quenched inactive galaxies whose star formation histories are dominated by the effects of downsizing at earlier epochs, a secondary effect for the AGN host galaxies. We show that histories of rapid quenching cannot account fully for the quenching of all the star formation in a galaxy's lifetime across the population of quenched AGN host galaxies, and that histories of slower quenching, attributed to secular (non-violent) evolution, are also key in their evolution. This is in agreement with recent results showing both merger-driven and non-merger processes are contributing to the co-evolution of galaxies and supermassive black holes. The availability of gas in the reservoirs of a galaxy, and its ability to be replenished, appear to be the key drivers behind this co-evolution.

12 pages, 11 figures