First uses of integrals ever in history?

Asked Sep 22 '17 at 10:59

Active Sep 22 '17 at 10:59

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What are the 3 first uses ever of integrals in history, and for which specific reasons were they used for? (formalized, so I'm not speaking about Archimedes attempts to calculate areas, 3rd century BC)

I guess it would be something like:

Newton (date?) (maybe for a mechanics/physics problem, which one exactly?)
Leibniz (date?) (for which problem?)
...

asked Sep 22 '17 at 10:59

Basj

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All right, so you are not “speaking about Archimedes attempts to calculate areas” (by the way, it wasn't merely an attempt; he did compute them). So, what are you speaking about? Do the areas computed by islamic mathematicians around 1000 AD count? After all, they used Archimedes as a role model. What about areas computed by Fermat? Or Isaac Barrow? – José Carlos Santos Sep 22 '17 at 11:03
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Bonaventura Cavalieri, Gilles Personne de Roberval... – FDP Sep 22 '17 at 11:07
@JoséCarlosSantos I mean in a formalized way, with the integral sign, etc. – Basj Sep 22 '17 at 11:11
Integral sign: Leibniz. – Mauro ALLEGRANZA Sep 22 '17 at 11:13
@Basj So, you are not interested in the first integrations. What you are interested in are the first uses of the integral sign. – José Carlos Santos Sep 22 '17 at 11:13
@Basj so you mean who introduced the symbol? modern formalization of these early ideas began as late as the nineteenth century, when people started to think more axiomatically about the reals. – M. Van Sep 22 '17 at 11:14
For dates, see the pos based-on-what-criteria-one-could-say-leibniz-invented-the-differential-calculus. – Mauro ALLEGRANZA Sep 22 '17 at 11:15
For some useful references to dates and precursoes, see the post when-was-the-inverse-relationship-between-tangents-and-quadrature-area-first-identified – Mauro ALLEGRANZA Sep 22 '17 at 11:18
See also why-are-integrals-called-integrals – Mauro ALLEGRANZA Sep 22 '17 at 11:23
And see why-was-the-term-integral-used-to-represent-the-area-under-a-curve. – Mauro ALLEGRANZA Sep 22 '17 at 11:24

First uses of integrals ever in history?

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