In this exercise, we work with a discrete problem and show why the relationship is analogous to

In this exercise, we work with a discrete problem and show why the relationshipmakes sense. Suppose we have a set of equally spaced grid points {a = x₀ < x₁ < x₂ < . . . x_{n - 1} < x_n = b}, where the distance between any two grid points is Δx. Suppose also that at each grid point xk, a function value f(x_k) is defined, for k = 0, . . ,n.

a. We now replace the integral with a sum and replace the derivative with a difference quotient. Explain whyis
analogous to

b. Simplify the sum in part (a) and show that it is equal to f(b) - f(a).

c. Explain the correspondence between the integral relationship and the summation relationship.

Transcribed Image Text:

| Sas"(x) dx = f(b) – f(a) Sås"(x) dx a.