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ERIC Number: EJ781057
Record Type: Journal
Publication Date: 2008-Jan
Pages: 8
Abstractor: Author
Reference Count: 10
ISSN: ISSN-0020-739X
Justifying Differential Derivations when Setting Up Definite Integrals
Tarvainen, K.
International Journal of Mathematical Education in Science and Technology, v39 n1 p61-68 Jan 2008
This paper addresses the forming of integral expressions such as [integral][superscript b][subscript a]f(x)dx by differential or infinitesimal derivations. A rigorous justification of these handy informal derivations is a major pedagogical problem in calculus. In this paper, checks are presented by which one can usually verify--with clear geometrical and physical considerations--that integral expressions obtained by differential derivations are correct. Thereby students who are used to rigorous mathematics can begin to trust streamlined differential derivations that are commonly used in physics and engineering. One check is for integrals of one function, another similar check is for the case where the integrand is a product of two functions. It is also shown that, in these checks, so called second-order terms can be left out. (Contains 3 figures.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A