b The midpoint rule does not compute an integral / f(a:) dac exactly. The error is the difference between the midpoint rule estimate Mn and the actual a 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 an) : (an i 3)4 on the interval [1,5]. Compute f\"(:13) : @.. What is the maximum value of |fl/(a:)l on the interval [1, 5] ? The error bound on Mn, as a function of n, is therefore B(n) : lg 5 Therefore. to be sure that Mn is within 10'3 of the true value of the integral / (:1; i 3)4 d9). we need B(n) S 10T3. which means we must choose 1 n: @- (Round up to the nearest integer.)