# A novel alternative to numerical integration

## TL;DR

This paper introduces a new method for numerical integration based on solving a differential equation, providing a more economical and accurate alternative to traditional quadrature techniques like Gauss and DE methods.

## Contribution

It proposes a novel approach that leverages the Fundamental Theorem of Calculus to compute integrals by solving a simple differential equation.

## Key findings

- The method is more economical than traditional quadrature methods.
- It achieves higher accuracy in numerical integration.
- Demonstrated effectiveness across various examples.

## Abstract

The Fundamental Theorem of Integral Calculus links the integrand and its antiderivative via a simple first order differential equation. A numerical solution of this ode yields the antiderivative and hence the required integral. This approach offers an economical and accurate alternative to the conventional approaches like the Gauss and the Double Exponential (DE) quadratures as demonstrated by a variety of examples.