# 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 {fn} on [a,b] converges pointwise on [a,b] to a Riemann integrable function f and if the functions {fn} are all bounded by a constant K on [a,b], then the limit of the integrals of the functions fn 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.