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I need help/advice with an dirac-delta integral. I computed the integral seen in the attachment and got 1. However, I am not quite sure if I did it right. Also, I don´t know how to throw this kind of integral with vectors in wolfram alpha.

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1 Attachment
So, does this integral equal 1?
Isn't the area under the curve of the dirac delta function always equal to 1?

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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??
I don't know if this helps or not. Seems like y^2... not sure...
@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.
I couldn't make head or tals out of it \[ \int_{\mathfrak{ R^3}} \delta(x-y)x^2 dx \; \text{wobei} \; y = (0,1,2)^T \] Usually vector surface integrals are like \[\iint_s \vec F(x,y,z) \cdot d\vec s \] where 's' is some region of surface like plane or cylinder and F is vector valued function. ]
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

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