Επαναληπτική άσκηση 9.

Έστω f : [0,+\infty) \rightarrow \mathbb{R} παραγωγίσιμη. Αν f(0)=0 και 0 < f'(x) < 1 για κάθε x > 0 να δείξετε ότι :

\int_{0}^{x}f^{3}(t)dt < (\int_{0}^{x}f(t)dt)^{2} για κάθε x > 0.

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