How students describe infinitesimal sources and infinitesimal spaces in integrals
written by
Gregory Mulder, Paul J. Emigh, and Elizabeth Gire
Many students who have completed a full year of calculus continue to demonstrate a weak understanding of the role of the infinitesimal in an integral. This lack of understanding has implications for learning in introductory calculus-based physics, where students must integrate contributions from spatially-distributed sources. Symbolically, a student who constructs such an integral in terms of small chunks of sources, like dm or dq, will need to relate their infinitesimal to a small chunk of space, like dx. In order to better understand how students use the integration infinitesimal, we collected and analyzed written solutions from 39 upperdivision physics majors who solved for the electric field at an asymmetric point in space above a homogeneously charged bar. We have identified several categories of ways students handled the infinitesimal when constructing an integral. We present evidence, supporting prior work, that a small segment understanding of the infinitesimal leads students to a correct translation from dq to dx.
Physics Education Research Conference 2018
Part of the PER Conference series Washington, DC: August 1-2, 2018
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![]() <a href="https://www.compadre.org/portal/items/detail.cfm?ID=14827">Mulder, G, P. Emigh, and E. Gire. "How students describe infinitesimal sources and infinitesimal spaces in integrals." Paper presented at the Physics Education Research Conference 2018, Washington, DC, August 1-2, 2018.</a>
![]() G. Mulder, P. Emigh, and E. Gire, , presented at the Physics Education Research Conference 2018, Washington, DC, 2018, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974).
![]() G. Mulder, P. Emigh, and E. Gire, How students describe infinitesimal sources and infinitesimal spaces in integrals, presented at the Physics Education Research Conference 2018, Washington, DC, 2018, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974>.
![]() Mulder, G., Emigh, P., & Gire, E. (2018, August 1-2). How students describe infinitesimal sources and infinitesimal spaces in integrals. Paper presented at Physics Education Research Conference 2018, Washington, DC. Retrieved May 3, 2025, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974
![]() Mulder, G, P. Emigh, and E. Gire. "How students describe infinitesimal sources and infinitesimal spaces in integrals." Paper presented at the Physics Education Research Conference 2018, Washington, DC, August 1-2, 2018. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974 (accessed 3 May 2025).
![]() Mulder, Gregory, Paul Emigh, and Elizabeth Gire. "How students describe infinitesimal sources and infinitesimal spaces in integrals." Physics Education Research Conference 2018. Washington, DC: 2018. of PER Conference. 3 May 2025 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974>.
![]() @inproceedings{
Author = "Gregory Mulder and Paul Emigh and Elizabeth Gire",
Title = {How students describe infinitesimal sources and infinitesimal spaces in integrals},
BookTitle = {Physics Education Research Conference 2018},
Address = {Washington, DC},
Series = {PER Conference},
Month = {August 1-2},
Year = {2018}
}
![]() %A Gregory Mulder %A Paul Emigh %A Elizabeth Gire %T How students describe infinitesimal sources and infinitesimal spaces in integrals %S PER Conference %D August 1-2 2018 %C Washington, DC %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974 %O Physics Education Research Conference 2018 %O August 1-2 %O application/pdf ![]() %0 Conference Proceedings %A Mulder, Gregory %A Emigh, Paul %A Gire, Elizabeth %D August 1-2 2018 %T How students describe infinitesimal sources and infinitesimal spaces in integrals %B Physics Education Research Conference 2018 %C Washington, DC %S PER Conference %8 August 1-2 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=14827&DocID=4974 Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.
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