1
$\begingroup$

I'd like to look at this problem in terms of the definite integral $I = \int_0^5 e^{\sin\sqrt x}dx$, and in terms of the Midpoint Rule. (Then, hopefully, I'll be able to figure out the left-point rule, right-point, Simpson's, and Trapezoidal.)

When the number of intervals increases by a factor of $q$, the approximation error decreases by a factor of $r(q)$, where $r$ depends on the particular method (let's try the Midpoint Rule). How do you determine the function $r$ theoretically?

  • 0
    I am not familiar with Euler-Maclaurin. I'm in the middle of learning the Taylor series (and the Maclaurin series)... thoughts on giving me some direction?2011-11-02

1 Answers 1

1

Okay. I figured out that the whole idea is applying the error bounds formula by subbing in "qn" for "n" and seeing how the resulting error changes.