let-f-t-0-arctan-e-tx-2-x-2-dx-with-t-gt-0-1-study-the-existence-of-f-t-2-calculate-f-t-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 35584 by abdo mathsup 649 cc last updated on 20/May/18

let f(t) = ∫_0 ^∞ ((arctan(e^(−tx^2 ) ))/x^2 ) dx with t>0 1) study the existence of f(t) 2) calculate f^′ (t)

$${let}\:\:{f}\left({t}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{arctan}\left({e}^{−{tx}^{\mathrm{2}} } \right)}{{x}^{\mathrm{2}} }\:{dx}\:{with}\:{t}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{study}\:\:{the}\:{existence}\:{of}\:\:{f}\left({t}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({t}\right) \\ $$

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let-f-t-0-arctan-e-tx-2-x-2-dx-with-t-gt-0-1-study-the-existence-of-f-t-2-calculate-f-t-

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