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Math Help - Difference of right and left Riemann sum

  1. #1
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    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.
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  2. #2
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    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)).
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