In Calculus, how do you get ci in Riemann sum formula?

Question

As in ci is the term that goes into the function.

http://archives.math.utk.edu/visual.calculus/4/riemann_sums.4/

Its the formula with the greek letter sigma.

Does that help? Its xi (the i is sub) instead of ci.

Answer 1

???? I don't understand your question, could you clarify so that I can help you?

OK. Exactly what was said in the next answer, except that it's not the sums, but the integral that doesn't depend on the choice of the ci s. Regardless how you choose the tag points ci, the integral of f over [a, b] is I if, for every eps >0, there exists a partition Peps of [a, b], such that if P is any refinement of Peps, then |S(f, [a,b], ci) - I| < eps. |S(f, [a,b], ci) is the Riemann sum coresponding to f , [a,b] and the points ci

Answer 2

According to Wikipedia, the choice for the xi (or ci) is arbitrary: you can pick any number in the interval.
If you take for xi the center of each subinterval, the sum is called the "middle Riemann sum". (see the graphs linked below for other examples)

If the function is "Riemann integrable", then the sum does not depend on the choices of the xi.