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

[kushan]

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

 

[sunjin09]

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

 

[kushan]

Can you please explain more

 

[sunjin09]

∫xdy=xy-∫ydx, you can move [x] into the integrand