Question Number 35212 by abdo mathsup 649 cc last updated on 16/May/18
$${prove}\:{by}\:{using}\:{series}\:{only}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{2}} \right){dx}=\:\int_{\mathrm{0}} ^{\infty} {sin}\left({x}^{\mathrm{2}} \right){dx}. \\ $$