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. The Riemann integral is unsuitable for many theoretical purposes. For a great many functions and practical applications, the Riemann integral can also be readily evaluated by using the fundamental theorem of calculus or (approximately) by numerical integration.
Some of the technical deficiencies in Riemann integration can be remedied by the Riemann–Stieltjes integral, and most of these disappear with the Lebesgue integral.
Read more about Riemann Integral: Overview, Examples, Similar Concepts, Integrability, Generalizations
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