Proving an identity of Dirac's delta function

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SUMMARY

The discussion focuses on proving the identity of Dirac's delta function as presented in the equation from Wolfram MathWorld. The user, Chen, seeks to start with the integral definition of the delta function and apply a change of variables from u to g(x). The challenge lies in effectively manipulating the integral to reach the desired identity. This highlights the complexities involved in working with distributions and variable transformations in mathematical proofs.

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Chen
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Hello,

I need to prove (7) here:
http://mathworld.wolfram.com/DeltaFunction.html

http://mathworld.wolfram.com/images/equations/DeltaFunction/equation5.gif

The instructions were to start with the definition of the delta function by integral, and then chagne variables u -> g(x). But I couldn't get anywhere really.

Thanks,
Chen
 
Last edited by a moderator:
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Never mind.
 

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