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Integral f^2,g^2=1 => f(c)+g(c)<=2 - OIMU 1998 Problem 1

Source:

September 12, 2010

calculusintegrationfunctioninequalitiesreal analysisreal analysis unsolved

Problem Statement

The definite integrals between

0

and

1

of the squares of the continuous real functions

f(x)

and

g(x)

are both equal to

1

. Prove that there is a real number

c

such that

f(c)+g(c)\leq 2