On the convergence of some improper integral of Terry's problem

TL;DR

This paper investigates the convergence of a specific improper integral related to Terry's problem in two dimensions, utilizing algebraic geometry techniques to analyze surfaces and their areas.

Contribution

It demonstrates the convergence of a special integral in Terry's problem using algebraic varieties and surface area estimations.

Findings

Proves convergence of the integral in two-dimensional Terry's problem.

Employs algebraic geometry methods for integral analysis.

Provides estimations of algebraic surface areas.

Abstract

In the article it was shown the convergence of special integral of two dimensional Terry's problem. Main tools of the article are an investigation of real algebraic varieties and estimations of areas of algebraic surfaces.