MathDB
Math constest 1

Source: Unirea 2005

February 8, 2005
integrationinequalitiesparameterizationfunctionreal analysisreal analysis solved

Problem Statement

a>0a>0 f:[−a,a]→Rf:[-a,a]\rightarrow R such that f′′f'' exist and Riemann-integrable suppose f(a)=f(−a)f(a)=f(-a) f′(−a)=f′(a)=a2 f'(-a)=f'(a)=a^2 Prove that 6a3≤∫−aaf′′(x)2dx6a^3\leq \int_{-a}^{a}{f''(x)}^2dx Study equality case ? Radu Miculescu
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