Abstract
The Riemann–Darboux integral is defined and integrable functions are studied. Principal results include the fundamental theorem of calculus. Nuggets include Riemann sums, volumes and surfaces of revolution.
Any segment of a section of a right angled cone [i.e. a parabola] is four-thirds of the triangle which has the same base and equal height
Archimedes. The method of mechanical theorems
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Notes
- 1.
The name “Riemann’s condition” appears in the book “Mathematical Analysis” by T. Apostol. I do not know of any other author who names it after Riemann. It is, however, convenient to have a name for it.
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Magnus, R. (2020). Integrals and Integration. In: Fundamental Mathematical Analysis. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-46321-2_6
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DOI: https://doi.org/10.1007/978-3-030-46321-2_6
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