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Taking Limits Under the Integral Sign

by F. Cunningham Jr. (Bryn Mawr College)

Year of Award: 1968

Publication Information: Mathematics Magazine, vol. 40, 1967, pp. 179-186

Summary: The author proves that if a sequence of Riemann integrable functions \(\{f_n\}\) on \([a,b]\) converges pointwise on \([a,b]\) to a Riemann integrable function \(f\) and if the functions \(\{f_n\}\) are all bounded by a constant \(K\) on \([a,b]\), then the limit of the integrals of the functions \(f_n\) over [a,b] is the integral of the function \(f\) over \([a,b]\).

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About the Author: (from Mathematics Magazine, vol. 40, (1967)) Frederick Cunningham, Jr. was at Bryn Mawr College at the time of publication.

Subject classification(s): Calculus | Single Variable Calculus | Integration
Publication Date: 
Wednesday, September 24, 2008

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