## TomLikesPhysics 2 years ago 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.

1. TomLikesPhysics

2. TomLikesPhysics

So, does this integral equal 1?

3. Kainui

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

4. TomLikesPhysics

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

5. Kainui

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

6. experimentX

is that triple integral??

7. Kainui

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

8. TomLikesPhysics

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

9. experimentX

10. experimentX

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

11. TomLikesPhysics

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

12. experimentX

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

13. TomLikesPhysics

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

14. experimentX

i see you have a point