let-f-x-0-e-x-t-sin-xt-dt-with-x-gt-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-U-n-

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}