Integral

: This article deals with the concept of an integral in calculus. For other meanings of "integral" see integration and integral (disambiguation).

Definitions of the integral

The most important integrals are the Riemann integral and the Lebesgue integral. The Riemann integral was created by Bernhard Riemann in 1854 and was the first rigorous definition of the integral. The Lebesgue integral was created by Henri Lebesgue to integrate a wider class of functions and to prove very strong theorems about interchanging limits and integrals.

Related Topics:
Riemann integral - Lebesgue integral - Bernhard Riemann - 1854 - Rigor - Henri Lebesgue - Theorem - Limit

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Although the Riemann and Lebesgue integrals are the most important ones, a number of others exist, including but not limited to:

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• The Daniell integral.
• The Darboux integral, a variation of the Riemann integral.
• The Denjoy integral (also known as the Henstock-Kurzweil integral), an extension of both the Riemann and Lebesgue integrals.
• The Haar integral.
• The Henstock-Kurzweil integral, an extension of both the Riemann and Lebesgue integrals (also called HK-integral).
• The Henstock-Kurzweil-Stieltjes integral (also called HK-Stieltjes integral).
• The Lebesgue-Stieltjes integral (also called Lebesgue-Radon integral).
• The Perron integral, which is equivalent to the restricted Denjoy integral.
• The Riemann-Stieltjes integral, an extension of the Riemann integral.