A measurement of the single-top-quark t-channel production cross section in pp collisions at root s = 7TeV with the CMS detector at the LHC is presented. Two different and complementary approaches have been followed. The first approach exploits the distributions of the pseudorapidity of the recoil jet and reconstructed top-quark mass using background estimates determined from control samples in data. The second approach is based on multivariate analysis techniques that probe the compatibility of the candidate events with the signal. Data have been collected for the muon and electron final states, corresponding to integrated luminosities of 1.17 and 1.56 fb(-1), respectively. The single-top-quark production cross section in the t-channel is measured to be 67.2 +/- 6.1 pb, in agreement with the approximate next-to-next-to-leading-order standard model prediction. Using the standard model electroweak couplings, the CKM matrix element vertical bar V-tb vertical bar is measured to be 1.020 +/- 0.046 (meas.) +/- 0.017 (theor.).