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Question Number 155264 by SANOGO last updated on 28/Sep/21

$$enutilisant{l}^{\prime }integraledecauchyschwarz$$$$l^{\prime }integrale{\int }_o^1\frac{f\left(x\right)}{x+1}dxestmajoreepar?$$$$$$

Answered by puissant last updated on 28/Sep/21

$$D^{\prime }apresAugustinluisCauchy,ona:$$$${\int }_0^1\frac{f\left(x\right)}{x+1}dx⩽{\left({\int }_0^1{f}^2\left(x\right)dx\right)}^{\frac{1}{2}}{\left({\int }_0^1\frac{1}{{(x+1)}^2}dx\right)}^{\frac{1}{2}}$$$$\Rightarrow {\int }_0^1\frac{f\left(x\right)}{x+1}dx⩽\frac{1}{2}\sqrt{{\int }_0^1{f}^2\left(x\right)dx}...$$

Commented by SANOGO last updated on 28/Sep/21

$$toujourslepuissant$$

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