Saturday at 9:19 PM Thread starter Admin #1 anemone MHB POTW Director Staff member Feb 14, 2012 3,632 Prove that for every $x\in (0,\,1)$ the following inequality holds: $\displaystyle \int_0^1 \sqrt{1+(\cos y)^2} dy>\sqrt{x^2+(\sin x)^2}$

Prove that for every $x\in (0,\,1)$ the following inequality holds: $\displaystyle \int_0^1 \sqrt{1+(\cos y)^2} dy>\sqrt{x^2+(\sin x)^2}$