Riemann Sum Calculus Question

Question

What is the subscript i of x in the Riemann Sum or Riemann Sum formula?

Answer 1

If the formula is left-side sum for i = 1 to n of y(x_i) Δx , it approximates the integral of f(x) from a to b and

Δx = (b-a)/n, then n is the number of rectangles whose areas are being added together. The x_i are the left sides of the the rectangles that go from x₀ (=a) to x_n (= b- Δx) and every intermediate x_i = a + Δx*i.

summations can be based on the right side, the average of the sides, or f(x) for the midpoint of the sides. All of which have slightly different summations in terms of indices. However, n rectangles are always summed.