We use 4 galaxies from the Calar Alto Legacy Integral Field Area ( CALIFA ) survey with clear signs of accretion onto supermassive black holes to investigate the relative contribution of star-formation and active galactic nucleus ( AGN ) activity to the line-emission of each galaxy as a function of radius . The combination of star-formation and AGN activity produces curved “ mixing sequences ” on standard optical diagnostic diagrams , and the fraction of emission due to AGN activity decreases smoothly with distance from the centre of the galaxy . We use the AGN activity profiles to calculate the size of the AGN narrow line regions , which have radii of \sim 6.3 kpc . We calculate the fractional contribution of the star-formation and the AGN activity to the global H \alpha , [ O II ] \lambda \lambda 3727,3729 and [ O III ] \lambda 5007 luminosities of each galaxy , and show that both ionization sources contribute significantly to the emission in all three lines . We use weighted combinations of stellar and AGN photoionization models to produce mixing models , which are consistent with observations for 85 percent of spaxels across the galaxies in our sample . We also present a new diagnostic for starburst-AGN mixing which requires only the [ O II ] , [ O III ] and H \beta emission lines , and can therefore be used to calculate AGN fractions up to z \sim 0.85 in the optical and z \sim 3.5 in the near-infrared . We anticipate that this diagnostic will facilitate studies of the properties of AGN ionizing radiation fields and the relative optical contribution of star-formation and AGN activity over cosmic time .