Abstract
The process of integration has ancient origins. Archimedes derived formulas for the areas of several kinds of figures by ingenious arguments based on the “method of exhaustion,” whereby a figure is approximated by finite unions of simpler figures whose areas are known. Such methods ultimately evolved into a form of heuristic reasoning, which is still used in each of the sciences to establish mathematical expressions for various quantities; not only length, area, and volume in geometry, but also mass, moments, electrical charge, power, yield from an investment, population, and many others.
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© 1994 Springer Science+Business Media New York
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Pedrick, G. (1994). Integration. In: A First Course in Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8554-5_6
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DOI: https://doi.org/10.1007/978-1-4419-8554-5_6
Publisher Name: Springer, New York, NY
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