Streamlining applications of integration by parts in teaching applied calculus

William Guo; William Guo

doi:10.3934/steme.2022005

STEM Education

2022, Volume 2, Issue 1: 73-83. doi: 10.3934/steme.2022005

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Classroom note

Streamlining applications of integration by parts in teaching applied calculus

William Guo ^,

School of Engineering and Technology, Central Queensland University, Bruce Highway, North Rockhampton, QLD 4702, Australia

Academic Editor: Gaifang Dong

Received: 01 November 2021 Revised: 01 January 2022

Integration by parts can be applied in various ways for obtaining solutions for different types of integrations and hence it is taught in all calculus courses in the world. However, the coverage and discourse of various applications of integration by parts in most textbooks, often packed into one section, lack a cohesion of progression for solving different types of integrals. Students may be confused by such incohesive presentation of the method and applications in the textbooks. Based on the author's experiences and practices in teaching applied calculus for undergraduate engineering and education students since 2013, a streamlined approach in teaching integration by parts has been gradually developed to the current state and ready to be shared with the mathematics teaching and learning communities. This streamlined approach allows integration by parts to be applied to solve complicated and integrated problems in a progressive way so that students can improve efficacy in their use of integration by parts gradually. This approach also makes communications easier with students on particular problems involving integration by parts.
- integration by parts,
- nested approach,
- cyclic approach,
- reduction formula,
- streamline
Citation: William Guo. Streamlining applications of integration by parts in teaching applied calculus[J]. STEM Education, 2022, 2(1): 73-83. doi: 10.3934/steme.2022005

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Abstract

Integration by parts can be applied in various ways for obtaining solutions for different types of integrations and hence it is taught in all calculus courses in the world. However, the coverage and discourse of various applications of integration by parts in most textbooks, often packed into one section, lack a cohesion of progression for solving different types of integrals. Students may be confused by such incohesive presentation of the method and applications in the textbooks. Based on the author's experiences and practices in teaching applied calculus for undergraduate engineering and education students since 2013, a streamlined approach in teaching integration by parts has been gradually developed to the current state and ready to be shared with the mathematics teaching and learning communities. This streamlined approach allows integration by parts to be applied to solve complicated and integrated problems in a progressive way so that students can improve efficacy in their use of integration by parts gradually. This approach also makes communications easier with students on particular problems involving integration by parts.

References

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