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TomLikesPhysics

  • 3 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.

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  1. TomLikesPhysics
    • 3 years ago
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  2. TomLikesPhysics
    • 3 years ago
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    So, does this integral equal 1?

  3. Kainui
    • 3 years ago
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    Isn't the area under the curve of the dirac delta function always equal to 1?

  4. TomLikesPhysics
    • 3 years ago
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    Yes, but it is a little bit different if you multiply it with another function, like here.

  5. Kainui
    • 3 years ago
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    Well it's beyond my knowledge, that was literally all I knew about the dirac delta function lol.

  6. experimentX
    • 3 years ago
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    is that triple integral??

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

  8. TomLikesPhysics
    • 3 years ago
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    @experimentX No but it is a vector integral in R2.

  9. experimentX
    • 3 years ago
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    what is your surface??

  10. experimentX
    • 3 years ago
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    as for Delta-Dirac, \[ \int_p^q \delta {(t - a)} f(t) dt = f(a) \; \text{ where a} \in (p, q)\]

  11. TomLikesPhysics
    • 3 years ago
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    @experimentX My integral looks a bit harder than your example. You can see it in the attachment.

  12. experimentX
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    i see you have a point

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