Difference of right and left Riemann sum

• Aug 25th 2012, 07:37 PM
feifan
Difference of right and left Riemann sum
Why is it that Rn-Ln = $\Delta x$(f(b)-f(a)) on [a,b]? I've tried manipulating summations but I can't seem to figure it out.
• Aug 26th 2012, 12:36 AM
Vlasev
Re: Difference of right and left Riemann sum
The simplest way is to say that except for the first summand of $L_n$ (it is $f(a)\Delta x$) and the last summand of $R_n$ (it is $f(b)\Delta x$), all the other terms appear in both sums. When you subtract, you are left with $R_n - L_n = \Delta x (f(b)-f(a))$.