A Simplified Approach to Students’ Learning of Equivalent Solutions to Some Integral Calculus Problems

Mary Olukemi Odumosu; Philip Ajibola Bankole

doi:doi:10.11648/j.dmath.20180301.13

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A Simplified Approach to Students’ Learning of Equivalent Solutions to Some Integral Calculus Problems

Mary Olukemi Odumosu, Philip Ajibola Bankole

Published in International Journal of Discrete Mathematics (Volume 3, Issue 1)

Received: 31 March 2018 Accepted: 17 April 2018 Published: 10 May 2018

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Abstract

This paper presents simple approach to determine an Equivalent Solutions to some Integral Calculus Problems. An experimental study was carried out on one hundred and twenty (120) students offering Integral Calculus Course in the Department of Mathematics, Adeniran Ogunsanya College of Education, Otto/Ijanikin, Lagos State. The sample chosen includes male and female students from the following course combinations: Physics / Mathematics, Chemistry / Mathematics, Computer / Mathematics, Integrated Science / Mathematics, Economics / Mathematics, Biology/Mathematics and Geography / Mathematics. The students were grouped into seven based on their course combinations. The students in their respective groups were subjected to the same problem on integration where they are free to use any method of integration of their choice. The students came up with various solutions to a given integral calculus problem. Each of the solutions obtained in each group was evaluated on specified interval to determine the numerical value in order to draw inference on equivalent solutions. Maple software was used to determine if the solutions from each group are equivalent or differs. The numerical value and graphical representation of the solutions from each group using Maple software shows that the solutions obtained by the students in their respective groups are equivalent. Hence, maple software adaptation in teaching integral calculus enhanced the students’ learning and by extension shows that equivalent solutions to some problems on integral calculus exists.

Published in	International Journal of Discrete Mathematics (Volume 3, Issue 1)
DOI	10.11648/j.dmath.20180301.13
Page(s)	21-27
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Integral Calculus, Methods of Integration, Equivalent Solutions, Maple Software, Graphical Representation of Solutions

References

[1]	Jr., W. P., & Miller, J. D. Pathways to an engineering career. Peabody Journal of Education, 2012, 87(1), 46-61.
[2]	Ebele C. Okigbo and Abigail M. Osuafor, Effect of using mathematics laboratory in teaching mathematics on the achievement of mathematics students. Educational Research and Review, 2008, Vol.3(8), pp.257-261, http://www.academicjournals.org/ERR ISSN 1990-3839.
[3]	Robert Wrede, and Murray R. Spiegel, Advanced Calculus, Third Edition, Schaum’s Outline Series,, McGraw-Hill Companies, Inc. 2010.
[4]	Tuan, S. A. and Effandi, Z. Enhancing Students’ Understanding in Integral Calculus through the Integration of Maple in Learning. Procedia - Social and Behavioral Sciences 102 (2013) 204 – 211.
[5]	Mark Zegarelli, Calculus II for Dummies, 2nd Edition, 2012.
[6]	Leah, Edelstein-Keshet, Integral Calculus: Mathematics 103, University of British Columbia, 2010, pp. 1-234.
[7]	Brian, S. Thompson. The Calculus Integral, ClassicalRealAnalysis.com (2010), [ISBN 1442180951].
[8]	Mary, Barnes, Introduction to Integration Part 2: The Definite Integral, University of Sydney, 1999, pp. 1-26.
[9]	Miguel A. L., Notes on Calculus II Integral Calculus, Northwestern University, Fall 2002. http://www.math.northwestern.edu/~mlerma/courses/math214-2-02f/.
[10]	www.kshitj-iitjee.com/maths/integrals/properties-of-definite-integrals.aspx

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Mary Olukemi Odumosu, Philip Ajibola Bankole. (2018). A Simplified Approach to Students’ Learning of Equivalent Solutions to Some Integral Calculus Problems. International Journal of Discrete Mathematics, 3(1), 21-27. https://doi.org/10.11648/j.dmath.20180301.13

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Mary Olukemi Odumosu; Philip Ajibola Bankole. A Simplified Approach to Students’ Learning of Equivalent Solutions to Some Integral Calculus Problems. Int. J. Discrete Math. 2018, 3(1), 21-27. doi: 10.11648/j.dmath.20180301.13

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Mary Olukemi Odumosu, Philip Ajibola Bankole. A Simplified Approach to Students’ Learning of Equivalent Solutions to Some Integral Calculus Problems. Int J Discrete Math. 2018;3(1):21-27. doi: 10.11648/j.dmath.20180301.13

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@article{10.11648/j.dmath.20180301.13,
  author = {Mary Olukemi Odumosu and Philip Ajibola Bankole},
  title = {A Simplified Approach to Students’ Learning of Equivalent Solutions to Some Integral Calculus Problems},
  journal = {International Journal of Discrete Mathematics},
  volume = {3},
  number = {1},
  pages = {21-27},
  doi = {10.11648/j.dmath.20180301.13},
  url = {https://doi.org/10.11648/j.dmath.20180301.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20180301.13},
  abstract = {This paper presents simple approach to determine an Equivalent Solutions to some Integral Calculus Problems. An experimental study was carried out on one hundred and twenty (120) students offering Integral Calculus Course in the Department of Mathematics, Adeniran Ogunsanya College of Education, Otto/Ijanikin, Lagos State. The sample chosen includes male and female students from the following course combinations: Physics / Mathematics, Chemistry / Mathematics, Computer / Mathematics, Integrated Science / Mathematics, Economics / Mathematics, Biology/Mathematics and Geography / Mathematics. The students were grouped into seven based on their course combinations. The students in their respective groups were subjected to the same problem on integration where they are free to use any method of integration of their choice. The students came up with various solutions to a given integral calculus problem. Each of the solutions obtained in each group was evaluated on specified interval to determine the numerical value in order to draw inference on equivalent solutions. Maple software was used to determine if the solutions from each group are equivalent or differs. The numerical value and graphical representation of the solutions from each group using Maple software shows that the solutions obtained by the students in their respective groups are equivalent. Hence, maple software adaptation in teaching integral calculus enhanced the students’ learning and by extension shows that equivalent solutions to some problems on integral calculus exists.},
 year = {2018}
}

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TY  - JOUR
T1  - A Simplified Approach to Students’ Learning of Equivalent Solutions to Some Integral Calculus Problems
AU  - Mary Olukemi Odumosu
AU  - Philip Ajibola Bankole
Y1  - 2018/05/10
PY  - 2018
N1  - https://doi.org/10.11648/j.dmath.20180301.13
DO  - 10.11648/j.dmath.20180301.13
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 21
EP  - 27
PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.dmath.20180301.13
AB  - This paper presents simple approach to determine an Equivalent Solutions to some Integral Calculus Problems. An experimental study was carried out on one hundred and twenty (120) students offering Integral Calculus Course in the Department of Mathematics, Adeniran Ogunsanya College of Education, Otto/Ijanikin, Lagos State. The sample chosen includes male and female students from the following course combinations: Physics / Mathematics, Chemistry / Mathematics, Computer / Mathematics, Integrated Science / Mathematics, Economics / Mathematics, Biology/Mathematics and Geography / Mathematics. The students were grouped into seven based on their course combinations. The students in their respective groups were subjected to the same problem on integration where they are free to use any method of integration of their choice. The students came up with various solutions to a given integral calculus problem. Each of the solutions obtained in each group was evaluated on specified interval to determine the numerical value in order to draw inference on equivalent solutions. Maple software was used to determine if the solutions from each group are equivalent or differs. The numerical value and graphical representation of the solutions from each group using Maple software shows that the solutions obtained by the students in their respective groups are equivalent. Hence, maple software adaptation in teaching integral calculus enhanced the students’ learning and by extension shows that equivalent solutions to some problems on integral calculus exists.
VL  - 3
IS  - 1
ER  -

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Author Information

Mary Olukemi Odumosu

Department of Mathematics, Adeniran Ogunsanya College of Education, Lagos, Nigeria
Philip Ajibola Bankole

Department of Mathematics, Adeniran Ogunsanya College of Education, Lagos, Nigeria

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Plain Text BibTeX RIS

APA Style

Mary Olukemi Odumosu, Philip Ajibola Bankole. (2018). A Simplified Approach to Students’ Learning of Equivalent Solutions to Some Integral Calculus Problems. International Journal of Discrete Mathematics, 3(1), 21-27. https://doi.org/10.11648/j.dmath.20180301.13

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ACS Style

Mary Olukemi Odumosu; Philip Ajibola Bankole. A Simplified Approach to Students’ Learning of Equivalent Solutions to Some Integral Calculus Problems. Int. J. Discrete Math. 2018, 3(1), 21-27. doi: 10.11648/j.dmath.20180301.13

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AMA Style

Mary Olukemi Odumosu, Philip Ajibola Bankole. A Simplified Approach to Students’ Learning of Equivalent Solutions to Some Integral Calculus Problems. Int J Discrete Math. 2018;3(1):21-27. doi: 10.11648/j.dmath.20180301.13

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@article{10.11648/j.dmath.20180301.13,
  author = {Mary Olukemi Odumosu and Philip Ajibola Bankole},
  title = {A Simplified Approach to Students’ Learning of Equivalent Solutions to Some Integral Calculus Problems},
  journal = {International Journal of Discrete Mathematics},
  volume = {3},
  number = {1},
  pages = {21-27},
  doi = {10.11648/j.dmath.20180301.13},
  url = {https://doi.org/10.11648/j.dmath.20180301.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20180301.13},
  abstract = {This paper presents simple approach to determine an Equivalent Solutions to some Integral Calculus Problems. An experimental study was carried out on one hundred and twenty (120) students offering Integral Calculus Course in the Department of Mathematics, Adeniran Ogunsanya College of Education, Otto/Ijanikin, Lagos State. The sample chosen includes male and female students from the following course combinations: Physics / Mathematics, Chemistry / Mathematics, Computer / Mathematics, Integrated Science / Mathematics, Economics / Mathematics, Biology/Mathematics and Geography / Mathematics. The students were grouped into seven based on their course combinations. The students in their respective groups were subjected to the same problem on integration where they are free to use any method of integration of their choice. The students came up with various solutions to a given integral calculus problem. Each of the solutions obtained in each group was evaluated on specified interval to determine the numerical value in order to draw inference on equivalent solutions. Maple software was used to determine if the solutions from each group are equivalent or differs. The numerical value and graphical representation of the solutions from each group using Maple software shows that the solutions obtained by the students in their respective groups are equivalent. Hence, maple software adaptation in teaching integral calculus enhanced the students’ learning and by extension shows that equivalent solutions to some problems on integral calculus exists.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - A Simplified Approach to Students’ Learning of Equivalent Solutions to Some Integral Calculus Problems
AU  - Mary Olukemi Odumosu
AU  - Philip Ajibola Bankole
Y1  - 2018/05/10
PY  - 2018
N1  - https://doi.org/10.11648/j.dmath.20180301.13
DO  - 10.11648/j.dmath.20180301.13
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 21
EP  - 27
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20180301.13
AB  - This paper presents simple approach to determine an Equivalent Solutions to some Integral Calculus Problems. An experimental study was carried out on one hundred and twenty (120) students offering Integral Calculus Course in the Department of Mathematics, Adeniran Ogunsanya College of Education, Otto/Ijanikin, Lagos State. The sample chosen includes male and female students from the following course combinations: Physics / Mathematics, Chemistry / Mathematics, Computer / Mathematics, Integrated Science / Mathematics, Economics / Mathematics, Biology/Mathematics and Geography / Mathematics. The students were grouped into seven based on their course combinations. The students in their respective groups were subjected to the same problem on integration where they are free to use any method of integration of their choice. The students came up with various solutions to a given integral calculus problem. Each of the solutions obtained in each group was evaluated on specified interval to determine the numerical value in order to draw inference on equivalent solutions. Maple software was used to determine if the solutions from each group are equivalent or differs. The numerical value and graphical representation of the solutions from each group using Maple software shows that the solutions obtained by the students in their respective groups are equivalent. Hence, maple software adaptation in teaching integral calculus enhanced the students’ learning and by extension shows that equivalent solutions to some problems on integral calculus exists.
VL  - 3
IS  - 1
ER  -

Copy | Download