My Math Forum A "simple" application of dirac delta "shift theorem"...help

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 February 13th, 2012, 11:45 AM #1 Newbie   Joined: Feb 2012 Posts: 1 Thanks: 0 A "simple" application of dirac delta "shift theorem"...help 1. The problem statement, all variables and given/known data show that for a, b, c, d positive: ?(a/b-c/d) = bd?(ad-bc) 2. Relevant equations ?f(x)?(x-a)dx = f(a) 3. The attempt at a solution Ok so I start with ??(a/b-c/d)f(x)dx But I am not sure how to apply the shift theorem. It seems I need to somehow relate a/b and x so that I can get it in the form of the shift theorem. But trying integration by substitution I always get tangled up. If I let u=a/b, then I can't relate dx to du to intergrate. If I just say let's call a/b as "x". then dx = what? ugh, this is a simple problem too. Seems like its an easy canditate for one of the first proofs shown after learning about the shift theorem so I feel pretty dumb that I'm not sure even where to start...

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