# 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 $[a,b]$.