let f(x) =∫_0 ^∞ e^(−x[t]) sin(xt)dt with x>0 1) find a explicit form for f(x) 2) let U_n =nf(n) find lim_(n→+∞) U_n and study the convergence of ΣU


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Question Number 58212 by maxmathsup by imad last updated on 20/Apr/19

$l e t f (x) = \int_{0}^{\infty} e^{- x [t]} s i n (x t) d t w i t h x > 0$ $1) f i n d a e x p l i c i t f o r m f o r f (x)$ $2) l e t U_{n} = n f (n) f i n d {l i m}_{n \to + \infty} U_{n} a n d s t u d y t h e c o n v e r g e n c e o f Σ U_{n}$
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