Hello...

I need to calculate this integral using the limit of the summation.

The period [0,T] is split into N intervals and the value point is at the left ot the interval.

Can someone please help?

Many Thanks to Galactus for his yesterday's idea but I believe my problem was not well posed.

I know the solution for something very similar:

This is verifiable using the trick 2ab= (a+b)^2 -a^2 -b^2 and making a=X(i), b=X(i+1)-X(i)

Straight, basic telescopic series come out and give the result.