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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/bc/d) = bd?(adbc) 2. Relevant equations ?f(x)?(xa)dx = f(a) 3. The attempt at a solution Ok so I start with ??(a/bc/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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application, delta, dirac, shift theoremhelp, simple 
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