A model is given for constructing artificial integrated spectral lines which allows the inclusion of all effects relevant to the synthesis of these lines by numerical methods. Among the effects included are noise, limb darkening, the centre-to-limb variation of the shapes and wavelength positions of the spectral line profiles, different laws of the differential rotation and a tilting of the rotating star. Fourier transformation of the artificial integrated spectral lines is applied to decide whether the different effects may influence the possibility of detecting stellar differential rotation by the method of Gray (1977).