The midpoint rule does not compute an integral / f(x) da exactly. The error is the difference between the midpoint rule estimate Mn and the actual value; we cannot find the actual error unless we can evaluate the integral exactly. We have a formula for an error bound on the midpoint rule, depending on f, a, b and n; we can calculate the error bound without evaluating the integral exactly. The important theorem is that the error on the estimate will always be less than or equal to the error bound, in absolute value. Consider f(a) = (x - 2)5 on the interval [1, 4]. Compute f" (x) = 20(x-2)^3 What is the maximum value of If (a) | on the interval [1, 4] ? |160 The error bound on Mn, as a function of n, is therefore B(n) = 180^2 Therefore, to be sure that Mn is within 10-2 of the true value of the integral (x - 2)5 da, we need B(n)