Differential rate of EMRIs ℱ_EMRI (solid lines) and of EMRIs and DPs ℱ_lc (dashed lines) as functions of energy. Quantities refer to a nuclear cluster with M_• = 3 × 10⁵ M_⊙ that has relaxed for 25 Myr (blue lines) and 45 Myr (orange lines). We report for reference vertical lines at the values of ℰ such that r_c(ℰ) is 0.1 R_inf (dash-dotted), 0.01 R_inf (dotted) and 0.001 R_inf (dashed). The colour-filled area of ℱ_lc gives the classical EMRI rate at r_c(ℰ) > 0.01 R_inf, to be compared with the hatched area of ℱ_EMRI over the full energy range. Apparent areas in the plot are proportional to the various integrals of the form ∫dℰ ℱ.