Question about the divergence theorem in hyperbolic space

Question

Let φ: M→H^(n+1) be an n-dimensional compact hypersurface embedding in the hyperbolic space. Denoting by N the interior normal vector to M in H^(n+1). My question is : Is it possible to compute ∫_M〈φ,N〉 dv In the Euclidean case, M is the boundary of a compact domain Ω of R^(n+1), and by applying the divergence theorem we obtain : ∫_M〈φ,N〉 dv=-(n+1)vol(Ω) So is it the same for the hyperbolic case?