How can [x] be moved into the integrand in the ∫ x^2 d[x] equation?

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Homework Help Overview

The discussion revolves around the integration of the function x^2 with respect to the greatest integer function, denoted as d[x], over the interval from -5 to 7. Participants are exploring how to manipulate the integrand in this context.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants are considering the implications of integrating with respect to the greatest integer function and discussing potential methods such as the use of delta functions or integration by parts. There are requests for further clarification on these approaches.

Discussion Status

The discussion is ongoing, with participants sharing different perspectives on how to approach the integration. Some have suggested specific mathematical techniques while others seek additional explanations.

Contextual Notes

There is a mention of potential ambiguity in the methods being considered, particularly regarding the interpretation of d[x] and its implications for the integration process.

kushan
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I was going through a book
Which had this question
∫ x^2 d[x] from -5 to 7

Which means integration wrt to greatest integer function of x
Any idea on how to go about it
 
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kushan said:
I was going through a book
Which had this question
∫ x^2 d[x] from -5 to 7

Which means integration wrt to greatest integer function of x
Any idea on how to go about it

d[x]=Ʃ_n δ(x-n) dx as far as I can see it ... or maybe integration by parts is less ambiguous
 
Last edited:
Can you please explain more
 
∫xdy=xy-∫ydx, you can move [x] into the integrand
 

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