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Aims. We aim to measure the physical properties of the hot X-ray corona of two active galactic nuclei, NGC 4388 and NGC 2110.
Methods. We analysed the hard X-ray (20-300keV) INTEGRAL spectrum in conjunction with archival XMM-Newton and NuSTAR data.
Results. The X-ray spectrum of both sources is phenomenologically well described by an absorbed cut-off power law. In agreement with previous results, we find no evidence of a Compton reflection component in these sources. We obtain a high-energy cut-off of 200_–40⁺⁷⁵keV for NGC 4388 and 320_–60⁺¹⁰⁰keV for NGC 2110. A fit with a thermal Comptonisation model yields a coronal temperature of 80_–20⁺⁴⁰keV and 75_–15⁺²⁰keV, respectively, and an optical depth of approximately two, assuming a spherical geometry. The coronal temperature and luminosity of both sources are consistent with pair production that acts as a thermostat for the thermal plasma. These results emphasise the importance of good signal-to-noise X-ray data above 100keV to probe the high-energy emission of AGNs.