  The initial mass function determines the fraction of stars of different
intial mass born per stellar generation. In this paper, we test the effects of
the integrated galactic initial mass function (IGIMF) on the chemical evolution
of the solar neighbourhood. The IGIMF (Weidner & Kroupa 2005) is computed from
the combination of the stellar intial mass function (IMF), i.e. the mass
function of single star clusters, and the embedded cluster mass function, i.e.
a power law with index beta. By taking into account also the fact that the
maximum achievable stellar mass is a function of the total mass of the cluster,
the IGIMF becomes a time-varying IMF which depends on the star formation rate.
We applied this formalism to a chemical evolution model for the solar
neighbourhood and compared the results obtained by assuming three possible
values for beta with the results obtained by means of a standard, well-tested,
constant IMF. In general, a lower absolute value of beta implies a flatter
IGIMF, hence a larger number of massive stars and larger metal ejection rates.
This translates into higher type Ia and II supernova rates, higher mass
ejection rates from massive stars and a larger amount of gas available for star
formation, coupled with lower present-day stellar mass densities. (abridged) We
also discuss the importance of the present day stellar mass function (PDMF) in
providing a way to disentangle among various assumptions for beta. Our results
indicate that the model adopting the IGIMF computed with beta ~2 should be
considered the best since it allows us to reproduce the observed PDMF and to
account for most of the chemical evolution constraints considered in this work.
