Consider a function consisting of a single rectangular pulse whose width is equal to w and amplitude is equal to 1/w. The integral (area) of the function is 1. Now consider the limit of the pulse, as w approaches zero. The integral (area) remains 1, but the amplitude approaches infinity. This is the Dirac Delta function.
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See h**p://www.sci.hkbu.edu.hk/msc/full/billy/node5.html
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Regards,
Kral