- Thread starter
- Admin
- #1
- Feb 14, 2012
- 3,802
Prove that for every $x\in (0,\,1)$ the following inequality holds:
$\displaystyle \int_0^1 \sqrt{1+(\cos y)^2} dy>\sqrt{x^2+(\sin x)^2}$
$\displaystyle \int_0^1 \sqrt{1+(\cos y)^2} dy>\sqrt{x^2+(\sin x)^2}$