The VISTA near infrared survey of the Magellanic System (VMC) will provide deep YJKs photometry reaching stars in the oldest turn-off point all over the Magellanic Clouds (MCs). As part of the preparation for the survey, we aim to access the accuracy
in the Star Formation History (SFH) that can be expected from VMC data, in particular for the LMC. To this aim, we first simulate VMC images containing not only the LMC stellar populations but also the foreground MW stars and background galaxies. We perform aperture photometry over these simulated images, access the expected levels of photometric errors and incompleteness, and apply the classical technique of SFH-recovery based on the reconstruction of colour-magnitude diagrams (CMD) via the minimization of a chi-squared-like statistics. We then evaluate the expected errors in the recovered star formation rate as a function of stellar age, SFR(t), starting from models with a known Age--Metallicity Relation (AMR). It turns out that, for a given sky area, the random errors for ages older than ~0.4 Gyr seem to be independent of the crowding. For a spatial resolution of ~0.1 sqdeg, the random errors in SFR(t) will be below 20% for this wide range of ages. On the other hand, due to the smaller stellar statistics for stars younger than ~0.4 Gyr, the outer LMC regions will require larger areas to achieve the same level of accuracy in the SFR(t). If we consider the AMR as unknown, the SFH-recovery algorithm is able to accurately recover the input AMR, at the price of an increase of random errors in the SFR(t) by a factor of about 2.5. Experiments of SFH-recovery performed for varying distance modulus and reddening indicate that the propagation of the errors in these parameters in the SFR(t) implies systematic errors below 30%.
