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Simpsons rule error bound.

  1. May 22, 2013 #1
    1. The problem statement, all variables and given/known data
    Calculate the value of n so that the approximation is within 0.0001. b = 2, a = 1. f(x) = 1/x.



    2. Relevant equations
    f4(x) = 24/x^5 (Think this is correct)
    Error <= (b-a)^5/180n^4(MAXx [a,b](f4(x))

    3. The attempt at a solution
    Well, 24/x^5 obtains it's max at x =1. Thus (MAXx [a,b](f4(x)) = 24.
    I subbed in all the given values and keep getting 6 as my answer. The correct answer is 8 though. Could somebody point out where I'm going wrong?
     
  2. jcsd
  3. May 22, 2013 #2

    Mark44

    Staff: Mentor

    What you wrote is ambiguous.
    Is it ((b - a)5/180) * n4 or
    (b - a)5/(180 * n4)?
     
  4. May 22, 2013 #3
    Apologies! It's (b-a)^5/(180*n^4).
     
  5. May 22, 2013 #4

    Mark44

    Staff: Mentor

    I get 6 as well. Is 8 the answer in the back of the book? It's possible they have the wrong answer.

    One way to check is to do Simpson's with n = 6, and compare the answer you get with the integral itself,
    $$\int_1^2 \frac{dx}{x} = ln(2) \approx. .69315$$

    You should have agreement in either 2 or 3 decimal places.
     
  6. May 22, 2013 #5
    Thanks for this too. There's most likely a mistake alright. I'll be sure to double check it in the morning though.
     
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