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I have a question about dirac-delta function. Integral of step function from -infinity to +infinity equals to infinity from the graph of step function.

[tex]\int_{-\infty}^{\infty}\theta (x) dx=\infty[/tex]

But calculating mathematically

[tex]\lim_{a\rightarrow\infty}\int_{-a}^{a}\theta(x) dx=\lim_{a\rightarrow\infty}(\delta \left(a \right)-\delta \left(-a\right))=0[/tex]

Because delta function is 0 except x=0. Please explain to me. Thanks

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# Integration of Step Function

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