The Computation of Derivatives of Trigonometric Functions via the Fundamental Theorem of Calculus

2005 ◽  
Vol 36 (2) ◽  
pp. 154
Author(s):  
Horst Martini ◽  
Walter Wenzel
Keyword(s):  
Fundamental Theorem ◽  
Trigonometric Functions ◽  
Fundamental Theorem Of Calculus ◽  
Derivatives Of

scholarly journals Analysis of a criterial examination of integral calculus: the case of a public university of Mexico

2021 ◽  
pp. 1-9
Author(s):  
Maximiliano DE LAS FUENTES-LARA ◽  
Wendolyn Elizabeth AGUILAR-SALINAS ◽  
Araceli Celina JUSTO-LÓPEZ
Keyword(s):  
Fundamental Theorem ◽  
Large Scale ◽  
Public University ◽  
Trigonometric Functions ◽  
Integral Calculus ◽  
Reliable Test ◽  
Fundamental Theorem Of Calculus ◽  
Integration Techniques ◽  
Logarithmic Functions ◽  
Research Show

This research analyzes the quality and results of a criterial and large-scale comprehensive calculus test in the school cycles between 2014 and 2019 to a total of 5367 second-semester students of the engineering careers of a mexican public university. With the results obtained it is observed that the criterial examination of integral calculus is a valid, reliable test with satisfactory power of discrimination and with a majority load of procedural reagents. The results of the research show that the greatest difficulty for students is focused on integration techniques, especially when trigonometric functions are involved. It was also found that the success of students in the ECCI is due to the ability to resolve integrals with hyperbolic, exponential and logarithmic functions, as well as the proper application of the fundamental theorem of calculus and the technique of variable change.

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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