The integrated elliptic flow of charged particles produced in Pb+Pb collisions at sNN−−−√=2.76 TeV has been measured with the ATLAS detector using data collected at the Large Hadron Collider. The anisotropy parameter, v2, was measured in the pseudorapidity range |η|≤2.5 with the event-plane method. In order to include tracks with very low transverse momentum pT, thus reducing the uncertainty in v2 integrated over pT, a 1 μb−1 data sample recorded without a magnetic field in the tracking detectors is used. The centrality dependence of the integrated v2 is compared to other measurements obtained with higher pT thresholds. The integrated elliptic flow is weakly decreasing with |η|. The integrated v2 transformed to the rest frame of one of the colliding nuclei is compared to the lower-energy RHIC data.