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So, does this integral equal 1?

Isn't the area under the curve of the dirac delta function always equal to 1?

Yes, but it is a little bit different if you multiply it with another function, like here.

Well it's beyond my knowledge, that was literally all I knew about the dirac delta function lol.

is that triple integral??

@experimentX
No but it is a vector integral in R2.

what is your surface??

as for Delta-Dirac,
\[ \int_p^q \delta {(t - a)} f(t) dt = f(a) \; \text{ where a} \in (p, q)\]

@experimentX
My integral looks a bit harder than your example. You can see it in the attachment.

Got it. In this case the delta function must be y and therefore the integral is 0^2+1^2+2^2=5.

i see you have a point