Applications of integrals

  • Adi Ben-Israel
  • Robert Gilbert
Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)


What do area, length, volume, work, and hydrostatic force have in common? All of these (and many other important concepts in science and engineering) can be modelled as Riemann sums (8.6)
$$\sum\limits_{k = 1}^n {f\left( {{\xi _k}} \right)} {\rm{ }}\Delta {x_k},$$
and computed as integrals (8.28),
$$\int\limits_{a}^{b} {f(x)dx: = \mathop{{\lim }}\limits_{{\parallel \mathcal{P}\parallel \to 0}} } \sum\limits_{{k = 1}}^{n} {f({{\xi }_{k}})\Delta {{x}_{k}}.}$$
In this chapter integrals are applied to problems of computing areas (Sects. 11.1, 11.2, and 11.6), arc lengths (Sect. 11.3), volumes (Sects. 11.4 and 11.5), moments and centroids (Sects. 11.7 and 11.8), work (Sect. 11.9), and hydrostatic force (Sect. 11.10).


Vertical Strip Power Stroke Dead Center Copper Base Compression Stroke 
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Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • Adi Ben-Israel
    • 1
  • Robert Gilbert
    • 2
  1. 1.Rutgers Center for Operations Research and Department of MathematicsRutgers UniversityNew BrunswickUSA
  2. 2.Department of Mathematical Science and Computer and Informational SciencesUniversity of DelawareNewarkUSA

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