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 lineemission 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 ∼ 6.3 kpc. We calculate the fractional contribution of the star-formation and the AGN activity to the global Hα, [O II] λλ 3727,3729 and [O III] λ 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 Hβ emission lines, and can therefore be used to calculate AGN fractions up to z ∼ 0.85 in the optical and z ∼ 3.5 in the nearinfrared. 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.