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Impossible integrals

Author:

McMahon, Casey Ray

Category:

Research Papers

Sub-Category:

Mathematical Physics

Language:

English

Date Published:

March 30, 2015

File:

/Research Papers-Mathematical Physics/Download/3682

Downloads:

1294

Keywords:

impossible integrals,tan(x)/x, sin(x)/x, cos(x)/x, integrals, elementary, non elementary, sinx/x, cosx/x, tanx/x

Abstract:

This paper attempts to show that non-elementary integrals can be expressed in an elementary way, by producing curves that closely approximate the true solution. Although there are a great many integrals that are considered impossible, in that they cannot be expressed in an elementary way, here I show that they can be approximated quite closely. I present a technique that allows for the generation of functions that closely approximate the solution to so-called non elementary integrals. I will only provide a small number of examples in this paper, although the technique can be applied to any integral, to give it an approximate elementary solution. It is my hope that from this work, a universal set of combinational approximating integral hybrids will be generated, and universally agreed upon, that may be used in conventional mathematics in place of non elementary solutions. In this paper, I shall evaluate the integrals ∫Sin(x)/(x) dx and ∫Cos(x)/(x) dx.

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