My question is really just a clarification. When using the Simpson's error equation to determine the value of n needed to produce a certain level of accuracy, you take the maximumabsolutevalue, right? So for instance, that means that for this problem:

$\displaystyle \int_{-1}^{2}\sqrt{1 + x^{2}}$

with

$\displaystyle f^{4}(x) = 3(4x^{2} - 1)(x^{2} + 1)^{-7/2}$

the maximum value of $\displaystyle |f^{4}(x)|$ on [-1,2] is theminimumof the function $\displaystyle f^{4}(x)$ on that interval, $\displaystyle f^{4}(x) = - 3$ at x = 0. So for

$\displaystyle |E_{n}|\leq \frac{(b-a)^{5}}{180n^{4}}K$

you use K = 3, right? Or do you use the actual maximum itself? (In the example, about $\displaystyle f^{4}(x)= 0.8463 $ at x = 0.866 or -0.886.) Thanks for the help!