MathDB
Today's calculation of Integral 843

Source: created by kunny

August 22, 2012
calculusintegrationfunctioninequalitiesspecial factorizationscalculus computations

Problem Statement

Let f(x)f(x) be a continuous function such that ∫01f(x) dx=1.\int_0^1 f(x)\ dx=1. Find f(x)f(x) for which ∫01(x2+x+1)f(x)2dx\int_0^1 (x^2+x+1)f(x)^2dx is minimized.
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