[en] Application of the functional integration method to obtain some characteristics of quantum mechanics system in the Euclidean formulation of theory is considered. The conditional Wiener integrals are calculated using our approximate formulas, which are exact for the functional polynomials of certain degree. The use of the method is demonstrated taking the anharmonic oscillator with Hsub(g)=1/2(psup(2)+xsup(2))+gxsup(4) and Hsup(f)=1/2(psup(2)+xsup(2))+1/2(xsup(2)-fsup(2))sup(2) as an example. The E₀, E₁ energies of the ground and first excited states of this system, propagator G(r)=<0|x(0)x(r)|0> and wave function squared of the ground state |phi₀(x)|² are calculated. The evaluation of the integrals is performed using the Gauss and Chebyshev quadrature formulas. The comparison of our numerical results with the values obtained by other authors using both Monte Carlo method on the lattice and approximation of paths in the Feynman integral is presented. This comparison demonstrates a higher efficiency of the method used