MathDB
Today's calculation of Integral 498

Source: created by kunny

October 13, 2009
calculusintegrationfunctioncalculus computations

Problem Statement

Let f(x) f(x) be a continuous function defined in the interval 0≤x≤1. 0\leq x\leq 1. Prove that \int_0^1 xf(x)f(1\minus{}x)\ dx\leq \frac{1}{4}\int_0^1 \{f(x)^2\plus{}f(1\minus{}x)^2\}\ dx.
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