let-give-F-t-0-sin-x-2-x-2-e-tx-2-dx-with-t-gt-0-find-dF-dt-t-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 28813 by abdo imad last updated on 30/Jan/18

let give F(t)=∫_0 ^∞ ((sin(x^2 ))/x^2 ) e^(−tx^2 ) dx with t>0 find (dF/dt)(t).

$${let}\:{give}\:{F}\left({t}\right)=\int_{\mathrm{0}} ^{\infty} \frac{{sin}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }\:{e}^{−{tx}^{\mathrm{2}} } {dx}\:\:{with}\:{t}>\mathrm{0} \\ $$$${find}\:\:\frac{{dF}}{{dt}}\left({t}\right). \\ $$$$ \\ $$

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