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 November 3rd, 2012, 12:55 PM #1 Member   Joined: Oct 2012 Posts: 36 Thanks: 0 integral proofing let f(x,t)=xe^(-xt).show that the integral I(x)=?f(x,t)dt (integration from 0 to infinite)exists for all x>=0 . is x->I(x) continuous on [0,infinite) what should i use here to prove the integral exist ???once i prove that exist, can i use the specific integration to see its continuity?????
 November 3rd, 2012, 10:26 PM #2 Senior Member   Joined: Jan 2012 From: Erewhon Posts: 245 Thanks: 112 Re: integral proofing Consider: $I_U(x)=\int_0^U x e^{-xt}\; dt$ Then $I(x)$ exists iff $\lim_{U \to \infty}I_U(x)$ exists, and when it does: $I(x)=\lim_{U\to \infty} I_U(x)$ CB
 November 6th, 2012, 02:50 PM #3 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: integral proofing Do Captain Black's $I_U$ with 'integration by parts'

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