# Numerical Integration

DevFeed: [Numerical Integration](<https://devfeed.tech/articles/numerical-integration-40253.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/01/08/numerical-integration/>)

Published: 2012-01-08T18:08:42Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [function](<https://devfeed.tech/topics/function.md>), [Code](<https://devfeed.tech/topics/code.md>)

Tags: [article](<https://devfeed.tech/tags/article.md>), [calculus](<https://devfeed.tech/tags/calculus.md>), [function](<https://devfeed.tech/tags/function.md>), [mathematica](<https://devfeed.tech/tags/mathematica.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [numerical-analysis](<https://devfeed.tech/tags/numerical-analysis.md>), [programming](<https://devfeed.tech/tags/programming.md>), [simpson-s-rule](<https://devfeed.tech/tags/simpson-s-rule.md>), [trapezoidal-rule](<https://devfeed.tech/tags/trapezoidal-rule.md>)

## AI overview

This article explains numerical integration by revisiting definite integrals, Riemann sums, and partition-based approximations. It introduces the problem of approximating a function's definite integral and begins with the left Riemann sum.

## Source excerpt

Rectangles, Trapezoids, and Simpson's I just wrapped up a semester of calculus TA duties, and I thought it would be fun to revisit the problem of integration from a numerical standpoint. In other words, the goal of this article is to figure out how fast we can approximate the definite integral of a function $ f:\mathbb{R} \to \mathbb{R}$. Intuitively, a definite integral is a segment of the area between a curve $ f$ and the $ x$-axis, where we allow area to be negative when $ f(x) < 0$.