The isospin-dependent quantum molecular dynamics (IDQMD) model is used to study the total reaction cross section σ_R. The energy-dependent Pauli volumes of neutrons and protons have been discussed and introduced into the IDQMD calculation to replace the widely used energy-independent Pauli volumes. The modified IDQMD calculation can reproduce the experimental σ_R well for both stable and exotic nuclei induced reactions. Comparisons of the calculated σ_R induced by ¹¹Li with different initial density distributions have been performed. It is shown that the calculation by using the experimentally deduced density distribution with a long tail can fit the experimental excitation function better than that by using the Skyrme-Hartree-Fock calculated density without long tails. It is also found that σ_R at high energy is sensitive to the long tail of density distribution.