On [0,1], let f have continuous derivatives satisfying 0<ƒ'(t)≤1. Also suppose ƒ(0)=0. Prove that (int_{0}^{1}ƒ(t)dt)^{2}≥int_{0}^{1}(ƒ(t))^{3}dt

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\[(\int\limits_{0}^{1}ƒ(t)dt)^{2}≥\int\limits_{0}^{1}(ƒ(t))^{3}dt \]

that's what it looks like

This is just the integral version of the Cauchy-Schwarz inequality.

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