We report a measurement of the top quark mass, mt, obtained from pp collisions at s√=1.96  TeV at the Fermilab Tevatron using the CDF II detector. We analyze a sample corresponding to an integrated luminosity of 1.9  fb−1. We select events with an electron or muon, large missing transverse energy, and exactly four high-energy jets in the central region of the detector, at least one of which is tagged as coming from a b quark. We calculate a signal likelihood using a matrix element integration method, where the matrix element is modified by using effective propagators to take into account assumptions on event kinematics. Our event likelihood is a function of mt and a parameter JES (jet energy scale) that determines in situ the calibration of the jet energies. We use a neural network discriminant to distinguish signal from background events. We also apply a cut on the peak value of each event likelihood curve to reduce the contribution of background and badly reconstructed events. Using the 318 events that pass all selection criteria, we find mt=172.7±1.8(stat+JES)±1.2(syst)  GeV/c2.