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We generalize Weyl's law to inhomogeneous bodies in $d$ dimensions. Using aperturbation scheme recently obtained by us in Ref. \cite{Amore09}, we havederived an explicit formula, which describes the asymptotic behavior of theeigenvalues of the negative laplacian on a closed $d$-dimensional cubic domain,either with Dirichlet or Neumann boundary conditions. For homogeneous bodies,the leading term in our formula reduces to the standard expression for Weyl'slaw. We have also used Weyl's conjecture to obtain a non-perturbative extensionof our formula and we have compared our analytical results with the precisenumerical results obtained using the Conformal Collocation Method of Refs.\cite{Amore08,Amore09}.

Can one hear the density of a drum? Weyl's law for inhomogeneous media