Question Number 35043 by math khazana by abdo last updated on 14/May/18
$${let}\:{t}>\mathrm{0}\:{and}\:{F}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{sin}\left({x}^{\mathrm{2}} \right)\:{e}^{−{tx}^{\mathrm{2}} } }{{x}^{\mathrm{2}} }{dx} \\ $$$${calculate}\:\frac{{dF}}{{dt}}\left({t}\right). \\ $$
Answered by MJS last updated on 14/May/18
$${F}'\left({t}\right)=−\underset{\mathrm{0}} {\overset{\infty} {\int}}\mathrm{sin}\left({x}^{\mathrm{2}} \right)\mathrm{e}^{−{x}^{\mathrm{2}} {t}} {dx} \\ $$