Suppose I have, $\int_{-\epsilon}^{\epsilon} \frac{\delta(x)}{x}dx= ?$
Now If I think of its asymmetric integrand, then ans is $0.$, Otherwise, it is $1/0=\infty$. (Divergent!)
Which ans I should consider. Pl help.
2026-03-31 20:11:34.1774987894
A doubt about an integration
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The integral is not convergent since $f(x)=1/x$ is not defined where $\delta(x)\neq0\iff x=0$.