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2015 | OriginalPaper | Chapter

16. Applications of Integration

Authors : Miklós Laczkovich, Vera T. Sós

Published in: Real Analysis

Publisher: Springer New York

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Abstract

One of the main goals of mathematical analysis, besides applications in physics, is to compute the measure of sets (arc length, area, surface area, and volume). We have already spent time computing arc lengths, but only for graphs of functions. We saw examples of computing the area of certain shapes (mostly regions under graphs), and at the same time, we got a taste of computing volumes when we determined the volume of a sphere (see item 2 in Example 13.23). We also noted, however, that in computing area, some theoretical problems need to be addressed (as mentioned in point 5 of Remark 14.10). In this chapter, we turn to a systematic discussion of these questions.

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Footnotes
1
Camille Jordan (1838–1922), French mathematician.
 
2
Paul Guldin (1577–1643), Swiss mathematician.
 
Literature
1.
go back to reference Davidson, K.R., Dosig, A.P.: Real Analysis and Applications. Theory in Practice. Springer, New York (2010) Davidson, K.R., Dosig, A.P.: Real Analysis and Applications. Theory in Practice. Springer, New York (2010)
2.
go back to reference Erdős, P., Surányi, J.: Topics in the Theory of Numbers. Springer, New York (2003) Erdős, P., Surányi, J.: Topics in the Theory of Numbers. Springer, New York (2003)
3.
go back to reference Euclid: The Thirteen Books of the Elements [Translated with introduction and commentary by Sir Thomas Heath]. Second Edition Unabridged. Dover, New York (1956) Euclid: The Thirteen Books of the Elements [Translated with introduction and commentary by Sir Thomas Heath]. Second Edition Unabridged. Dover, New York (1956)
4.
go back to reference Hewitt, E., Stromberg, K.: Real and Abstract Analysis. Springer, New York (1975) Hewitt, E., Stromberg, K.: Real and Abstract Analysis. Springer, New York (1975)
5.
go back to reference Niven, I., Zuckerman, H.S., Montgomery, H.L.: An Introduction to the Theory of Numbers, 5th edn. Wiley, New York (1991) Niven, I., Zuckerman, H.S., Montgomery, H.L.: An Introduction to the Theory of Numbers, 5th edn. Wiley, New York (1991)
6.
go back to reference Rademacher, H., Toeplitz, O.: Von Zahlen und Figuren. Springer, Berlin (1933) [English translation: The Enjoyment of Mathematics]. Dover, New York (1990) Rademacher, H., Toeplitz, O.: Von Zahlen und Figuren. Springer, Berlin (1933) [English translation: The Enjoyment of Mathematics]. Dover, New York (1990)
7.
go back to reference Rudin, W.: Principles of Mathematical Analysis, 3rd edn. McGraw-Hill, New York (1976) Rudin, W.: Principles of Mathematical Analysis, 3rd edn. McGraw-Hill, New York (1976)
8.
go back to reference Zaidman, S.: Advanced Calculus. An Introduction to Mathematical Analysis. World Scientific, Singapore (1997) Zaidman, S.: Advanced Calculus. An Introduction to Mathematical Analysis. World Scientific, Singapore (1997)
Metadata
Title
Applications of Integration
Authors
Miklós Laczkovich
Vera T. Sós
Copyright Year
2015
Publisher
Springer New York
DOI
https://doi.org/10.1007/978-1-4939-2766-1_16

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