Context. The current distribution of planet mass vs. incident stellar X-ray flux supports the idea that photoevaporation of the atmosphere may take place in close-in planets. Integrated effects have to be accounted for. A proper calculation of the mass loss rate through photoevaporation requires the estimation of the total irradiation from the whole XUV (X-rays and extreme ultraviolet, EUV) range. Aims: The purpose of this paper is to extend the analysis of the photoevaporation in planetary atmospheres from the accessible X-rays to the mostly unobserved EUV range by using the coronal models of stars to calculate the EUV contribution to the stellar spectra. The mass evolution of planets can be traced assuming that thermal losses dominate the mass loss of their atmospheres. Methods: We determine coronal models for 82 stars with exoplanets that have X-ray observations available. Then a synthetic spectrum is produced for the whole XUV range (~1-912 Å). The determination of the EUV stellar flux, calibrated with real EUV data, allows us to calculate the accumulated effects of the XUV irradiation on the planet atmosphere with time, as well as the mass evolution for planets with known density. Results: We calibrate for the first time a relation of the EUV luminosity with stellar age valid for late-type stars. In a sample of 109 exoplanets, few planets with masses larger than ~1.5 MJ receive high XUV flux, suggesting that intense photoevaporation takes place in a short period of time, as previously found in X-rays. The scenario is also consistent with the observed distribution of planet masses with density. The accumulated effects of photoevaporation over time indicate that HD 209458b may have lost 0.2 MJ since an age of 20 Myr. Conclusions: Coronal radiation produces rapid photoevaporation of the atmospheres of planets close to young late-type stars. More complex models are needed to explain the observations fully. Spectral energy distributions in the XUV range are made available for stars in the sample through the Virtual Observatory for the use in future planet atmospheric models. Appendices and Tables 3 and 4 are available in electronic form at http://www.aanda.org