We test the integrated galactic initial mass function (IGIMF) on the chemical evolution of 16 ultrafaint dwarf (UFD) galaxies discussing in detail the results obtained for three of them: Boötes I, Boötes II, and Canes Venatici I, taken as prototypes of the smallest and the largest UFDs. These objects have very small stellar masses (∼103-104 M☉) and quite low metallicities ([Fe/H] < -1.0 dex). We consider four observational constraints: the present-day stellar mass, the [α/Fe] versus [Fe/H] relation, the stellar metallicity distribution function and the cumulative star formation history. Our model follows in detail the evolution of several chemical species (H, He, α-elements, and Fe). We take into account detailed nucleosynthesis and gas flows (in and out). Our results show that the IGIMF, coupled with the very low star formation rate predicted by the model for these galaxies (∼10-4-10-6 M☉yr-1), cannot reproduce the main chemical properties, because it implies a negligible number of core-collapse SNe and even Type Ia SNe, the most important polluters of galaxies. On the other hand, a constant classical Salpeter IMF gives the best agreement with data, but we cannot exclude that other formulations of the IGIMF could reproduce the properties of these galaxies. Comparing with Galaxy data, we suggest that UFDs could not be the building blocks of the entire Galactic halo, although more data are necessary to draw firmer conclusions.
