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February 13th, 2012, 12:45 PM   #1
Joined: Feb 2012

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A "simple" application of dirac delta "shift theorem"

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


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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