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Math Help - Simpson's Rule Error Question

  1. #1
    Newbie ImprecantesStellam's Avatar
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    Simpson's Rule Error Question

    Hey everyone!

    So I'm given this equation:

    x e^(^-^0^.^2^(^x^2^)

    They want me to find the least number of sub-intervals required to get an accuracy of 10 ^-^8. In the first part of the problem, they ask me to get the max of the fourth derivative from an interval of 0 to 1, right? I take the derivatives until the fifth derivative, and I got my max to be: 0.975525220034 approximately, and yeah. Then, I'm looking back at my notes, and I see that my teacher gave us this formula to use to calculate the error of the Simpson's Rule:

     f^4(z) (b - a)^5 / (2880N^4)

    The problem specifically says to use 2 to find the smallest number of N sub intervals to get the Simpson Error to a 10 ^-^8 accuracy.

    So what I did was that I set up my equation like this:

     10 ^-^8 = f^4(2) (1-0)^5 / (2880N^4)

    and then I tried to solve for N, but I got this:

    0.0019835453.

    I can't possibly have that amount of sub intervals, so obviously I'm doing something wrong. I double-checked my differentiation with several people, and they said my differentiation was correct, so I just...I'm getting slightly frustrated. I don't understand what I'm doing wrong, and why I can't get a good value for N.

    If I can get any advice, guidance, or any help, I would greatly appreciate it!
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  2. #2
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    Re: Simpson's Rule Error Question

    I'm rusty at this but I'll give it a shot -

    Input 1 into your fourth derivative. Then multiply it by (b-a)^5 [should be 1 since 1^5 is 1.]. Then divide this by 180n^4. Get n to the other side and solve.
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  3. #3
    Newbie ImprecantesStellam's Avatar
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    Re: Simpson's Rule Error Question

    Quote Originally Posted by bhaktir View Post
    I'm rusty at this but I'll give it a shot -

    Input 1 into your fourth derivative. Then multiply it by (b-a)^5 [should be 1 since 1^5 is 1.]. Then divide this by 180n^4. Get n to the other side and solve.
    Alright, so when I do that, I get: 0.0333109337. The problem says to use two, so where does 2 come into play here?

    Sorry for asking so many questions; I'm just very confused. Normally, I'm pretty good at Calculus, but this is frustrating me. Moreover, why did you use 180 instead of 2880?
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  4. #4
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    Re: Simpson's Rule Error Question

    I think you're supposed to use 180. I could be wrong though.

    I'm just reviewing this stuff now, and I can't believe how much I've forgotten.
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