  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%.
