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Inequality involving area under a curve

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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,632
Prove that for every $x\in (0,\,1)$ the following inequality holds:

$\displaystyle \int_0^1 \sqrt{1+(\cos y)^2} dy>\sqrt{x^2+(\sin x)^2}$