On Some New Applications to Newton-Raphson Method

TL;DR

This paper introduces a novel technique leveraging the Newton-Raphson method to approximate areas under curves and develop a formula for definite integrals with high accuracy under specific conditions.

Contribution

It presents a new approximation technique for integrals using the Newton-Raphson method and a formula with minimal relative error for calculating areas under curves.

Findings

The new technique provides accurate area approximations.

The formula for definite integrals has very small relative error.

Applicable under certain mathematical conditions.

Abstract

I am going to provide a new technique of approximating area under the curve, using the Newton-Raphson Method. I am also going to provide a formula that would help us approximate any Definite Integral or help us find the area under the curve, under certain conditions. The relative error of this formula is very small, which makes it even more interesting.