• Title/Summary/Keyword: 미적분의 기본정리

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A Study on the Fundamental Theorem of Calculus : Focused on the Relation between the Area Under Time-velocity Graph and Distance (미적분의 기본정리에 대한 고찰 - 속도 그래프 아래의 넓이와 거리의 관계를 중심으로 -)

  • Joung, Youn-Joon;Lee, Kyung-Hwa
    • Journal of Educational Research in Mathematics
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    • v.19 no.1
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    • pp.123-142
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    • 2009
  • Dynamic context is considered as a source for intuitive understanding on the calculus. The relation between the area under time-velocity graph and distance is the base of the dynamic contexts which are treated in the integral calculus. The fundamental theorem of calculus has originated in dynamic contexts. This paper investigated the fundamental theorem of calculus via the relation between the area under time-velocity graph and distance. And we analyzed mathematics textbooks and the understanding of students. Finally we suggest some proposal for the teaching of the fundamental theorem of calculus.

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A study on the Relationship between Indefinite Integral and Definite Integral (부정적분과 정적분의 관계에 관한 고찰)

  • Joung, Youn-Joon;Lee, Kyeong-Hwa
    • School Mathematics
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    • v.11 no.2
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    • pp.301-316
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    • 2009
  • There are two distinct processes, definite integral and indefinite integral, in the integral calculus. And the term 'integral' has two meanings. Most students regard indefinite integrals as definite integrals with indefinite interval. One possible reason is that calculus textbooks do not concern the meaning in the relationship between definite integral and indefinite integral. In this paper we investigated the historical development of concepts of definite integral and indefinite integral, and the relationship between the two. We have drawn pedagogical implication from the result of analysis.

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