Results 251 to 260 of about 127,882 (296)
, 2010 In diesem Kapitel werden wir integrieren lernen und sehen, dass dies im gewissen Sinne das Gegenstuck zum Differenzieren aus Kapitel 11 darstellt. Wieso braucht man eigentlich einen Integralbegriff? Und was versteht man darunter? Und wieso nennen wir dies das Riemann-Integral? Gibt es andere Moglichkeiten, das Integral zu definieren? Fragen uber Fragen.
Florian Modler, Martin Kreh
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, 2016 In the previous chapter we reviewed differentiation—one of the two pillars of single variable calculus. The other pillar is, of course, integration, which is the focus of the current chapter. More precisely, we will turn to the definite integral, the integral of a function on a fixed interval, as opposed to the indefinite integral, otherwise known as ...
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2014
Since antiquity, people were interested in computing the length of curves, the area of surfaces, and the volumes of solids.
A. D. R. Choudary +1 more
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Since antiquity, people were interested in computing the length of curves, the area of surfaces, and the volumes of solids.
A. D. R. Choudary +1 more
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2015
Riemann integrals of functions are defined and the mean value theorem for integrals is proved. The relationship between integration and differentiation is uncovered in the fundamental theorem of calculus. The techniques of integration by substitution and by parts are established, and the latter is used to develop Stirling’s formula for the ...
Kee L. Teo +2 more
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Riemann integrals of functions are defined and the mean value theorem for integrals is proved. The relationship between integration and differentiation is uncovered in the fundamental theorem of calculus. The techniques of integration by substitution and by parts are established, and the latter is used to develop Stirling’s formula for the ...
Kee L. Teo +2 more
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, 1996 In this chapter we give an exposition of the definite integral of a real-valued function defined on a closed bounded interval. We assume familiarity with this concept from a previous study of calculus, but want to develop the theory in a more precise way than is typical for calculus courses, and also take a closer look at what kind of functions can be ...
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2003
As was pointed out in the previous chapter, the second fundamental topic covered in calculus is the Riemann integral, the first being the derivative.
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As was pointed out in the previous chapter, the second fundamental topic covered in calculus is the Riemann integral, the first being the derivative.
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, 2013 Here we consider the familiar integral from calculus which is generally attributed to Riemann, though the idea of upper and lower sums for finding areas was used previously by Cauchy; other mathematicians had used such sums before Cauchy for estimating integrals but not for calculating exact values.
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2001
The Fundamental Theorem of Calculus is a statement about the inverse relationship between differentiation and integration. It comes in two parts, depending on whether we are differentiating an integral or integrating a derivative. Under suitable hypotheses on the functions f and F, the Fundamental Theorem of Calculus states that $$ \begin{array}{l}
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The Fundamental Theorem of Calculus is a statement about the inverse relationship between differentiation and integration. It comes in two parts, depending on whether we are differentiating an integral or integrating a derivative. Under suitable hypotheses on the functions f and F, the Fundamental Theorem of Calculus states that $$ \begin{array}{l}
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