Kim et al. (2012) introduced an interestingp-adic analogue of the Eulerian polynomials. They studied some identities on the Eulerian polynomials in connection with the Genocchi, Euler, and tangent numbers. In this paper, by applying the symmetry of the fermionicp-adicq-integral on , defined by Kim (2008), we show a symmetric relation between theq-extension of the alternating sum of integer powers and the Eulerian polynomials.