Prove: $\displaystyle \int\limits_{0}^{1} f(x)^2 \mathrm{\,d}x \ge 4$

by 129492   Last Updated October 20, 2019 05:20 AM - source

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I need to prove the following integral inequality: $\displaystyle \int\limits_{0}^{1} f(x)^2 \mathrm{\,d}x \ge 4$. I have tried to use holder integral inequality but have no use. Can you help me to prove that?

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