Orderly exact calculation of integrals of products of functions by the method of tenzor products of functionals

The paper is devoted to approximate calculation of integrals of products of two functions by the method of tensor products of functionals. Under the assumption that one of them is from the Sobolev class with the dominant mixed derivative, and the other with fast oscillation, there are obtained unimprovable (in the sense of order) estimates of arising errors of approximation. Also, a comparative analysis with known methods in the "theory of oscillations" be conducted.