Exploration of parametric integrals related to a question of soil mechanics

ABSTRACT

We study a 1-parameter family of trigonometric definite integrals, showing how the joint usage of Information and Communication Technologies and paper-and-pencil work lead to different outputs, revealing different mathematical meanings and different concrete meanings. This family of integrals is useful for describing a phenomenon in soil mechanics, whence the importance of such integrals in STEM education.

KEYWORDS:

• Parametric integrals
• computer algebra system
• soil failure
• STEM

Acknowledgment

The authors wish to thank the anonymous referee for his/her useful remarks.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. STEM is an acronym for Science, Technology, Engineering, and Mathematics.

2. http://www.oeis.org.

3. URL: http://oeis.org/A025547.

4. URL: http://oeis.org/A007509.