Question

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.

Answer 1

So, does this integral equal 1?

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

is that triple integral??

Answer 6

I don't know if this helps or not. Seems like y^2... not sure... http://www.thefouriertransform.com/math/impulse.php

Answer 7

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

Answer 8

what is your surface??

Answer 9

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

Answer 10

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

Answer 11

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.
] http://tutorial.math.lamar.edu/Classes/CalcIII/SurfIntVectorField.aspx

Answer 12

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

Answer 13

i see you have a point