Thread: Integration of greatest integer function

Hello,

Originally Posted by champrock

Separate the integral :

if x is between 0 and 1, then [x]=0
if x is between 1 and 2, then [x]=1

so your integral is actually , if

if n=0, then the integral is

but its actually [X]^N whcih is most confusing. (mod raised to Nth power).

so, it cant be seperated that easily.

Originally Posted by champrock

but its actually [X]^N whcih is most confusing. (mod raised to Nth power).

so, it cant be seperated that easily.

It is... Because x varies from 0 to 1 and from 1 to 2.


x in [0,1[ => [x]=0 => [x]^n=0^n=0, if n is not equal to 0.
x in [1,2[ => [x]=1 => [x]^n=1^n=1.

hmm.. lets just take an example. assume that n=5 and x=1.5, then 1.5^5 = 7.59..

Let be an integer then

Hence, for it's which is the value of the integral.

Originally Posted by champrock

hmm.. lets just take an example. assume that n=5 and x=1.5, then 1.5^5 = 7.59..

But you're working with the greatest integer function !

It's [x]^n, not [x^n], that's certainly not the same...

what I showed you gives the exact same result as Krizalid. (apart from the case n=0)