  The nuclear medium effects are studied in the $\nu_\tau/\bar\nu_\tau$
interactions from nuclei in the deep inelastic scattering (DIS) region and
applied to the $^{40}Ar$ nucleus to obtain the scattering cross sections in the
energy region of the proposed DUNE experiment. The free nucleon structure
functions ($F_{iN}(x,Q^2);~(i=1-5)$) have been calculated at the
next-to-leading order (NLO) using Martin-Motylinski-Harland Lang-Thorne 2014 as
well as The Coordinated Theoretical-Experimental Project on QCD
parameterizations for parton distribution functions (PDFs) and including the
effect of perturbative and nonperturbative QCD corrections
\cite{Ansari:2020xne}. These free nucleon structure functions are then
convoluted with the nucleon spectral function in the nucleus to obtain the
nuclear structure functions ($F_{iA}(x,Q^2);~(i=1-5)$). The nucleon spectral
function takes into account the Fermi motion and the binding energy of the
nucleons as well as the nucleon correlations within the nucleus. These nuclear
structure functions are then used to calculate the deep inelastic scattering
cross sections. Moreover, the contribution of $\pi$ and $\rho$ mesons as well
as the corrections due to the shadowing and antishadowing effects in the
relevant kinematic region of the Bjorken variable $x$ are also included. The
numerical results for the cross sections have been presented and compared with
the results obtained in the phenomenological approach using nuclear structure
functions from nCTEQnu.
