  We consider the integrals of $r$-mean curvatures $S_r$ of a complete
hypersurface $M$ in space forms $\mathcal{Q}_c^{n+1}$ which generalize volume
$(r=0)$, total mean curvature $(r=1)$, total scalar curvature $(r=2)$ and total
curvature $(r=n)$. Among other results we prove that a complete properly
immersed hypersurface of a space form with
  $S_r\geq 0$, $S_r\not\equiv 0$ and $S_{r+1}\equiv 0$ for some $r\le n-1$ has
$\int_MS_rdM=\infty.$
