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Question Number 55643 by gunawan last updated on 01/Mar/19

$$\mathrm{known}\mathrm{function}f$$$$\mathrm{diferensiable}\mathrm{continues}\mathrm{at}[a,b]$$$$\mathrm{If}f\left(a\right)=f\left(b\right)=0$$$$\mathrm{and}$$$${\int }_a^b{\left[f\left(x\right)\right]}^{2}dx=1$$$$\mathrm{Prove}\mathrm{that}$$$${\int }_a^b{x}^2{\left[f^{\prime }\left(x\right)\right]}^{2}dx⩾\frac{1}{4}$$

Commented by tanmay.chaudhury50@gmail.com last updated on 01/Mar/19

$$\left[f\left(x\right)\right]\leftarrow is[.]greatestintegerfunctionor$$$$simplybracket...$$

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