Integral involving an integral part
I recently started working through Arfken, Weber and Harris' Mathematical Methods for Physicists, when I came across the following integral:
where is the integral part of .
I don't understand how the RHS emerges from the LHS. Can someone please enlighten me as to what the hidden steps are? Thanks very much.
Re: Integral involving an integral part
It looks pretty straight forward to me. One of the very first things you learn about integrals is that " ". I presume you will agree that . Extending that, the left side is equal to since that just breaks the integral into a sum of integrals. If x lies between n and n+ 1 then [x]= n so that .