Improved measurements of <i>D</i><SUP>0</SUP> → <i>K</i><SUP>-</SUP><i>l</i><SUP>+</SUP>ν<i>_l</i> and <i>D</i><SUP>+</SUP> → (<i>K</i>)over-bar<SUP>0</SUP><i>l</i><SUP>+</SUP>ν<i>_l</i>

Using 7.93 fb(-1) of e(+)e(-) collision data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we measure the absolute branching fractions of D-0 -> K(-)e(+)nu(e), D-0 -> K- mu(+)nu(mu), D+ -> (K) over bar (0) e(+)nu(e), and D+ -> (K) over bar (0) mu(+)nu(mu) to be (3.521 +/- 0.009(stat) +/- 0.016(syst))%, (3.419 +/- 0.011(stat) +/- 0.016(syst))%, (8.864 +/- 0.039(stat) +/- 0.082s(yst))%, and (8.665 +/- 0.046(stat) +/- 0.084(syst) )%, respectively. By performing a simultaneous fit to the partial decay rates of these four decays, the product of the hadronic form factor f(+)(K) (0) and the modulus of the c -> s Cabibbo-Kobayashi-Maskawa matrix element |V-cs| is determined to be f(+)(K) (0) |V-cs| = 0.7171 +/- 0.0011(stat) +/- 0.0013(syst). Taking the value of |V-cs| = 0.97349 +/- 0.00016 from the standard model global fit or that of f(+)(K) (0) = 0.7452 +/- 0.0031 from the lattice quantum chromodynamics calculation as input, we derive the results f(+)(K) (0) = 0.7366 +/- 0.0011(stat) +/- 0.0013(syst). and |V-cs| = 0.9623 +/- 0.0015(stat) +/- 0.0017(syst) +/- 0.0040LQCD.