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Hi,

Is the following integral well defined? If it is, then what does it evaluate to?

[tex] \int_{-1}^{1} \delta(x) \Theta(x) \mathrm{d}x [/tex]

where [itex]\delta(x)[/itex] is the dirac delta function, and [itex]\Theta(x)[/itex] is the the Heaviside step function.

What about if I choose two functions [itex]f_k[/itex] and [itex]g_k[/itex], which are such that [itex] f_k \rightarrow \delta(x) [/itex] and [itex] g_k \rightarrow \Theta(x) [/itex]? Will this integral converge? I understand that if i choose [itex]f_k[/itex] and [itex]g_k[/itex] such that [itex]f_k = g'_k[/itex] then this integral will evaluate to [itex]1/2[/itex], but what if i choose other independent representation of these functions?

Is the following integral well defined? If it is, then what does it evaluate to?

[tex] \int_{-1}^{1} \delta(x) \Theta(x) \mathrm{d}x [/tex]

where [itex]\delta(x)[/itex] is the dirac delta function, and [itex]\Theta(x)[/itex] is the the Heaviside step function.

What about if I choose two functions [itex]f_k[/itex] and [itex]g_k[/itex], which are such that [itex] f_k \rightarrow \delta(x) [/itex] and [itex] g_k \rightarrow \Theta(x) [/itex]? Will this integral converge? I understand that if i choose [itex]f_k[/itex] and [itex]g_k[/itex] such that [itex]f_k = g'_k[/itex] then this integral will evaluate to [itex]1/2[/itex], but what if i choose other independent representation of these functions?

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