My undergraduate system textbook has this property in the appendix
δ(x2−a2)=12|a|[δ(x−a)+δ(x+a)]
and I can't seem to derive the result
I tried the following:
∫∞−∞f(x)δ(x2−a2)dx
let u2=x2−a2 and x=√u2−a2 however I couldn't resolve the new limit of integral as u must be strictly positive under this substitution. What is another way I can approach this?
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