  We study a notion of non-commutative integration, in the spirit of modular
spectral triples, for the quantum group $SU_{q}(2)$. In particular we define
the non-commutative integral as the residue at the spectral dimension of a zeta
function, which is constructed using a Dirac operator and a weight. We consider
the Dirac operator introduced by Kaad and Senior and a family of weights
depending on two parameters, which are related to the diagonal automorphisms of
$SU_{q}(2)$. We show that, after fixing one of the parameters, the
non-commutative integral coincides with the Haar state of $SU_{q}(2)$. Moreover
we can impose an additional condition on the zeta function, which also fixes
the second parameter. For this unique choice the spectral dimension coincides
with the classical dimension.
