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Erschienen in:
2015 | OriginalPaper | Buchkapitel
16. Applications of Integration
verfasst von : Miklós Laczkovich, Vera T. Sós
Erschienen in: Real Analysis
Verlag: 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.