Recent years brought a new approach which seems to be quite powerful and utilizable with ease in numerical analysis. It is the fluctuationlessness approximation and, univariate or multivariate, an integral can be approximated through its kernel function's matrix representation by using not it but the image of the matrix representations of the independent variables under that integrand function. Method works well by giving good approximation qualities as long as the integrand behaves sufficiently smooth. Although the method seems to be superior to a lot of existing methods this smoothness related issue stands a problematic agent as in other methods. This work is devoted to the investigation of smoothening possibilities to the integrand.