The problem of approximate quadrature is one of the most studied problems in analysis. Emerging from the needs of computations associated with the solution of various applied problems, it has been extensively developed and has been the subject of numerous studies. The works in this field are exhaustive, but the study of the outside world poses new problems where seemingly everything is known. An example is the approximate quadrature formula for a complex function F(y₁, . . . , y_n)...

The spatial position of the borehole is usually determined by measuring its inclination 8k and azimuth fk at a number of points Mk, the distance Sk from the wellhead is known (k - 1, 2 . .). Such determination is reduced either to the calculation of the coordinates of the well axis, or to its graphical construction according to the measurement data ...

Over the last 20 years, new methods have been introduced in geodesic science, allowing to solve all the main problems of geodesy by the values characterizing the external gravitational field and the figure of the Earth's physical surface.In the non-pratial and complex physical surface of the Earth, a smooth surface close to Listing's geoid, called quasigeoid, is distinguished.

Until recently, the solution of the main task of higher geodesy - determination of the Earth's shape - was connected with the study of the external gravitational field and the shape of Listing's geoid. The only method of gravimetric derivation of the geoid's shape was the Stokes method, the application of which requires the removal of masses external to the geoid, the so-called regularization of the Earth.