![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Integral_as_region_under_curve.svg/640px-Integral_as_region_under_curve.svg.png&w=640&q=50)
Riemann integral
Basic integral in elementary calculus / From Wikipedia, the free encyclopedia
In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval. It was presented to the faculty at the University of Göttingen in 1854, but not published in a journal until 1868.[1] For many functions and practical applications, the Riemann integral can be evaluated by the fundamental theorem of calculus or approximated by numerical integration, or simulated using Monte Carlo integration.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Integral_as_region_under_curve.svg/640px-Integral_as_region_under_curve.svg.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/2/28/Riemann_integral_regular.gif/320px-Riemann_integral_regular.gif)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Riemann_integral_irregular.gif/320px-Riemann_integral_irregular.gif)