1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Trapezoidal Rule: Maximum error in approximation?

  1. Mar 12, 2016 #1
    1. The problem statement, all variables and given/known data
    Suppose that T4 is used to approximate the ∫ from 0 to 3 of f(x)dx, where -2 ≤ f ''(x) ≤ 1 for all x. What is the maximum error in the approximation?

    2. Relevant equations
    |ET|≤ (K(b-a)^3)/(12n^2)

    3. The attempt at a solution
    So I know how to find the error of the trapezoidal rule using the above equation, but I do not understand how to find the maximum error in an approximation.
    To find the max error I would find the max/mins of f ''(x), right? But I don't know how to do that when f(x) is not given
     
  2. jcsd
  3. Mar 12, 2016 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You can't. All you can do is find an upper bound on the absolute error, so your actual error may be a lot less than your bound. Just find an upper bound on ##|f''(x)|## over ##x \in [0,3]##.

    Note: people hardly ever find best bounds by finding actual maxima of things like ##|f''(x)|##; typically, they are satisfied with decent bounds.
     
  4. Mar 12, 2016 #3
    So K would just be 2?
     
  5. Mar 12, 2016 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You tell me.
     
  6. Mar 13, 2016 #5
    yes....:wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Trapezoidal Rule: Maximum error in approximation?
  1. Trapezoidal Rule (Replies: 3)

Loading...