In this paper, we give an integral approximation for the elliptic operators with
anisotropic coecients on smooth manifold. Using the integral approximation, the elliptic equation
is tranformed to an integral equation. The integral approximation preserves the symmetry and
coercivity of the original elliptic operator. Based on these good properties, we prove the convergence
between the solutions of the integral equation and the original elliptic equation.