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Possible Duplicate:
Prove that $\int_0^x f^3 \le \left(\int_0^x f\right)^2$

Let $f$ be a differentiable function on $[0,1]$. $f(0)=0$ and $1\ge f'(x)\ge0$. Show that

$\int_0^1f(x)^3dx\le\left(\int_0^1f(x)dx\right)^2$

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