## TomLikesPhysics Group Title 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. one year ago one year ago

1. TomLikesPhysics Group Title

2. TomLikesPhysics Group Title

So, does this integral equal 1?

3. Kainui Group Title

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

4. TomLikesPhysics Group Title

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

5. Kainui Group Title

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

6. experimentX Group Title

is that triple integral??

7. Kainui Group Title

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

8. TomLikesPhysics Group Title

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

9. experimentX Group Title

10. experimentX Group Title

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

11. TomLikesPhysics Group Title

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

12. experimentX Group Title

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 Group Title

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 Group Title

i see you have a point