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Integral
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An integral is the continuous analog of a sum, used to calculate areas, volumes, and their generalizations. The major advance in integration came in the 17th century with the independent discovery of the fundamental theorem of calculus by Leibniz and Newton, and Bernhard Riemann later gave a rigorous definition based on a limiting procedure, generalized by Henri Lebesgue in the early 20th century.
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1. MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and StatisticsLeibniz biography, 21 November 1675Quote, Leibniz biography, 21 November 1675
On 21 November 1675 he wrote a manuscript using the integral f(x)dx notation for the first time.
Integral (Wikipedia)
Wikimedia Foundationlead paragraph and history sectionQuote, lead paragraph and history section
The major advance in integration came in the 17th century with the independent discovery of the fundamental theorem of calculus by Leibniz and Newton.
Integral (Wikipedia)
Wikimedia FoundationIn Branch: Analysis, lead paragraphQuote, In Branch: Analysis, lead paragraph
The major advance in integration came in the 17th century with the independent discovery of the fundamental theorem of calculus by Leibniz and Newton.
Integral (Wikipedia)
Wikimedia FoundationAssociated With: Isaac Newton, lead paragraphQuote, Associated With: Isaac Newton, lead paragraph
The major advance in integration came in the 17th century with the independent discovery of the fundamental theorem of calculus by Leibniz and Newton.
Integral (Wikipedia)
Wikimedia FoundationAssociated With: Gottfried Wilhelm Leibniz, lead paragraphQuote, Associated With: Gottfried Wilhelm Leibniz, lead paragraph
The major advance in integration came in the 17th century with the independent discovery of the fundamental theorem of calculus by Leibniz and Newton.
Dissenting Readings (1 dissenting reading)
Associated With: Isaac Newton
The same priority dispute that attaches to the derivative attaches to the integral: Leibniz introduced the integral sign and worked out integration as the inverse of differentiation independently of Newton, publishing his methods from 1684 onward, years before Newton's own fluxional calculus appeared in print. Historians today treat the two as independent co-discoverers of both halves of the fundamental theorem of calculus, so crediting this edge to Newton alone, without its Leibniz counterpart edge on this same entity, understates a genuinely shared origin.
A dissenting reading, from Gottfried Wilhelm Leibniz and his supportersWikipedia: Leibniz-Newton Calculus Controversy, Wikimedia Foundation
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