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Question Number 102336 by 175mohamed last updated on 08/Jul/20

$$iff\left(x\right)⩽2l+1$$$$and{\int }_1^{3}f\left(x\right)dx⩽l^2$$$$findthevalueofl$$

Commented by mr W last updated on 08/Jul/20

$$nouniquesolution$$

Answered by PRITHWISH SEN 2 last updated on 08/Jul/20

$$\mathrm{let}{\mathrm{f}}_{\max }=2l+1\mathrm{at}\mathbf{x}=\mathbf{c}$$$$\therefore {\int }_1^3\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}⩽(3-1)\mathrm{f}\left(\mathrm{c}\right)=l^2$$$$\Rightarrow \mathrm{f}\left(\mathrm{c}\right)=\frac{l^2}{2}$$$$\therefore \frac{l^2}{2}=2l+1\Rightarrow l=2\pm \sqrt{6}\mathbf{please}\mathbf{check}$$

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