|February 13th, 2012, 12:45 PM||#1|
Joined: Feb 2012
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
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...
|application, delta, dirac, shift theoremhelp, simple|
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