# Taking Limits Under the Integral Sign

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 $$[a,b]$$.

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

MSC Codes:
97I50
Author(s):
F. Cunningham Jr. (Bryn Mawr College)
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Publication Date:
Wednesday, September 24, 2008
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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 $$[a,b]$$.