# A Tale of Two Integrals

by Vilmos Totik

Year of Award: 2000

Publication Information: The American Mathematical Monthly, vol. 106, 1999, pp. 227-240

Summary: This paper presents several approaches to a simple-looking combinatorial-analysis problem with the aim of showing how different ideas can lead to a solution.  The analysis version of the problem can be stated as follows: If $$f$$ and $$g$$ are functions each having integral over $$[0,1]$$ equal to $$1$$, then there is some subinterval of $$[0,1]$$ over which each integral is equal to $$1/2$$.