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To investigate the nature of the $\psi(3770)$ resonance and to measure thecross section for $e^+e^- \to D\bar{D}$, a cross-section scan data sample,distributed among 41 center-of-mass energy points from 3.73 to 3.89~GeV, wastaken with the BESIII detector operated at the BEPCII collider in the year2010. By analyzing the large angle Bhabha scattering events, we measure theintegrated luminosity of the data sample at each center-of-mass energy point.The total integrated luminosity of the data sample is$76.16\pm0.04\pm0.61$~pb$^{-1}$, where the first uncertainty is statistical andthe second systematic.

Measurement of the Integrated Luminosities of Cross-section Scan Data Samples Around the $\psi(3770)$ Mass Region