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Integrals of functions containing parameters

Published online by Cambridge University Press:  08 October 2020

Robert M. Corless
RCCA and Applied Mathematics, University of Western Ontario, London, Ontario, Canada e-mail:
David J. Jeffrey
ORCCA and Applied Mathematics, University of Western Ontario, London, Ontario, Canada e-mail:
David R. Stoutemyer
University of Hawaii, Honolulu, HI, USA e-mail:


Calculus students are taught that an indefinite integral is defined only up to an additive constant, and as a consequence generations of students have assiduously added ‘+C’ to their calculus homework. Although ubiquitous, these constants rarely garner much attention, and typically loiter without intent around the ends of equations, feeling neglected. There is, however, useful work they can do, work which is particularly relevant in the contexts of integral tables and computer algebra systems. We begin, therefore, with a discussion of the context, before returning to coax the constants out of the shadows and assign them their tasks.

© Mathematical Association 2020

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