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Question Number 35212 by abdo mathsup 649 cc last updated on 16/May/18
prove by using series only that   ∫_0 ^∞  cos(x^2 )dx= ∫_0 ^∞ sin(x^2 )dx.
$${prove}\:{by}\:{using}\:{series}\:{only}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{2}} \right){dx}=\:\int_{\mathrm{0}} ^{\infty} {sin}\left({x}^{\mathrm{2}} \right){dx}. \\ $$

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