Sharing Teaching Ideas: The Area under a Curve: Conjecturing the Fundamental Theorem of Calculus

2003 ◽  
Vol 96 (7) ◽  
pp. 474-478
Author(s):  
Jeff Suzuki
Keyword(s):  
Fundamental Theorem ◽  
Nctm Standards ◽  
Fundamental Theorem Of Calculus ◽  
Computer Technologies ◽  
Classroom Exercise ◽  
College Calculus ◽  
Teaching Ideas ◽  
Introductory College

The NCTM standards for courses designed to prepare students for the “new calculus” include using “all appropriate calculator and computer technologies,” as well as promoting “the use of experimentation and conjecturing” (NCTM 2000, p. 289). Both these goals can be met in the following experiment to find the area under a curve. The experiment is a modification of a classroom exercise that I conducted in an introductory college calculus course for nonmajors.

scholarly journals Integral transforms of the κ-Hilfer fractional derivative

2021 ◽  
Author(s):  
Felix Costa ◽  
Junior Cesar Alves Soares ◽  
Stefânia Jarosz
Keyword(s):  
Fractional Derivative ◽  
Gamma Function ◽  
Fundamental Theorem ◽  
Beta Function ◽  
Integral Transforms ◽  
Fractional Operators ◽  
Riesz Fractional Derivative ◽  
Hilfer Fractional Derivative ◽  
Fundamental Theorem Of Calculus

In this paper, some important properties concerning the κ-Hilfer fractional derivative are discussed. Integral transforms for these operators are derived as particular cases of the Jafari transform. These integral transforms are used to derive a fractional version of the fundamental theorem of calculus. Keywords: Integral transforms, Jafari transform, κ-gamma function, κ-beta function, κ-Hilfer fractional derivative, κ-Riesz fractional derivative, κ-fractional operators.

Teaching the Fundamental Theorem of Calculus: A Historical Reflection

2012 ◽  
Author(s):  
Jorge M. L��pez Fern��ndez ◽  
Omar A. Hern��ndez Rodr��guez
Keyword(s):  
Fundamental Theorem ◽  
Fundamental Theorem Of Calculus ◽  
Historical Reflection
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