Abstract
In the previous chapter of our book, we became acquainted with the concept of the indefinite integral: the collection of primitive functions of f was called the indefinite integral of f. Now we introduce a very different kind of concept that we also call integrals—definite integrals, to be precise. This concept, in contrast to that of the indefinite integral, assigns numbers to functions (and not a family of functions). In the next chapter, we will see that as the name integral that they share indicates, there is a strong connection between the two concepts of integrals.
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Notes
- 1.
Niels Henrik Abel (1802–1829), Norwegian mathematician.
- 2.
David Hilbert (1862–1943), German mathematician.
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Laczkovich, M., Sós, V.T. (2015). The Definite Integral. In: Real Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2766-1_14
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DOI: https://doi.org/10.1007/978-1-4939-2766-1_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2765-4
Online ISBN: 978-1-4939-2766-1
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