# Theory - Analytically should the smoothed value be exactly equal to the smoothed value?

Hello!

For fun I tried to apply the math as I understand it

But I am very unsure about the last step, i.e. the integral over the domain w.r.t. to the volume around particle i, should not just dissolve?

Could anyone explain my misunderstanding to me?

Kind regards

## Comments

Title was wrong, it should have been:

Analytically should the smoothed value be exactly equal to the exact value?

Basically I am asking how to prove this

For those who are stuck same place, look https://www.youtube.com/watch?v=fhpR6sqbcr8&t