• Title/Summary/Keyword: A definite integral formula

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A DEFINITE INTEGRAL FORMULA

  • Choi, Junesang
    • East Asian mathematical journal
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    • v.29 no.5
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    • pp.545-550
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    • 2013
  • A remarkably large number of integral formulas have been investigated and developed. Certain large number of integral formulas are expressed as derivatives of some known functions. Here we choose to recall such a formula to present explicit expressions in terms of Gamma function, Psi function and Polygamma functions. Some simple interesting special cases of our main formulas are also considered. It is also pointed out that the same argument can establish explicit integral formulas for other those expressed in terms of derivatives of some known functions.

On the Evaluation of a Vortex-Related Definite Trigonometric Integral

  • Lee, Dong-Kee
    • Journal of Ocean Engineering and Technology
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    • v.18 no.1
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    • pp.7-9
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    • 2004
  • Using the solution to th contour integral of the complex logarithmic function ${\oint}_cIn(z-z_{0})dz$, the following definite integral, derived from the formula to calculate the forces exerted to n circular cylinder by the discrete vortices shed from it, has been evaluated (equation omitted)

Comprehending the Symbols of Definite Integral and Teaching Strategy (정적분 기호 이해의 특징과 교수학적 전략)

  • Choi, Jeong-Hyun
    • Journal for History of Mathematics
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    • v.24 no.3
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    • pp.77-94
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    • 2011
  • This study aims to provide a teaching strategy accommodating the symbols of the definite integral and guiding students through the meaning of notations in area and volume calculations, based on characterization as to how students comprehend the symbols used in the Riemann sum formula and the definite integral, and their interrelationship. A survey was conducted on 70 high school students regarding the historical background of integral symbols and the textbook contents designated for the definite integral. In the following analysis, the comprehension was qualified by 5 levels; students in higher levels of comprehension demonstrated closer relation to the history of integral notations. A teaching strategy was developed accordingly, which suggested more desirable student understanding on the concept of definite integral symbols in area and volume calculations.

Uniformity in Highschool Mathematics Textbooks in Definite Integral and its applications\ulcorner (정적분과 응용- 교과서 내용의 균일성\ulcorner)

  • 석용징
    • Journal of Educational Research in Mathematics
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    • v.11 no.2
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    • pp.307-320
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    • 2001
  • Traditionally, there are many inherent restrictions in highschool mathematics textbooks. They are restricted in its contents and inevitably resorted to reader's ability of intuition. So they are usually lacked logical precisions and have various differences in expressions. We are mainly concerned with the definite integral and its applications in current highschool mathematics II textbooks according to 6th curriculum. We choose 6 of them arbitrarily and survey by comparison to deduce some controversial topics among them as follows. 1) absurd metaphors in formula process 2) confusions in important notations and too much choices in terms and statements. 3) lack of precisions in - teaching hierarchy (between some contents of Physics and the applications of definite integral) - introducing a proof of theorem (fundamental theorem of Calculus I) - introducing the methods (integral substitutions 1, ll) 4) adopting small topics such as - mean value theorem of integral - integrals with variable limits. In coming 7th curriculum, highschool students in Korea are supposed to choose calculus as a whole, independent course. So we hope that the suggested controversial topics are to be referred by authors to improve the preceding Mathematics ll textbooks and for teachers to use them for better mathematics education.

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SOME INTEGRAL REPRESENTATIONS OF THE CLAUSEN FUNCTION Cl2(x) AND THE CATALAN CONSTANT G

  • Choi, Junesang
    • East Asian mathematical journal
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    • v.32 no.1
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    • pp.43-46
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    • 2016
  • The Clausen function $Cl_2$(x) arises in several applications. A large number of indefinite integrals of logarithmic or trigonometric functions can be expressed in closed form in terms of $Cl_2$(x). Very recently, Choi and Srivatava [3] and Choi [1] investigated certain integral formulas associated with $Cl_2$(x). In this sequel, we present an interesting new definite integral formula for the Clausen function $Cl_2$(x) by using a known relationship between the Clausen function $Cl_2$(x) and the generalized Zeta function ${\zeta}$(s, a). Also an interesting integral representation for the Catalan constant G is considered as one of two special cases of our main result.