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Math Help - An unusual simpson's rule question

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    An unusual simpson's rule question

    Here is a question even the professor couldn't answer.
    Show that if f is a polynomial of degree three or lower, then Simpson's Rule gives the exact value of (a bottom) integral (b top) f(x)dx. I would appreciate an answer back as soon as possible. Thanks
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    Quote Originally Posted by desdemoniagirl View Post
    Here is a question even the professor couldn't answer.
    Show that if f is a polynomial of degree three or lower, then Simpson's Rule gives the exact value of (a bottom) integral (b top) f(x)dx. I would appreciate an answer back as soon as possible. Thanks
    Do you have a copy of Smith and Minton's "Calculus - Early Transcendentals". They discuss this on page 415 in the exploratory exercises.
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    Book error

    Hello, I dont have a copy of Smith's early transcendentals, but i do have a copy of Steward's early transcendentals. Do they give an explination, because I cant find it. thanks in advance
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    Quote Originally Posted by desdemoniagirl View Post
    Hello, I dont have a copy of Smith's early transcendentals, but i do have a copy of Steward's early transcendentals. Do they give an explination, because I cant find it. thanks in advance
    Well, you can look at the error bound E_s which is given by

    |E_s| \le \frac{K(b-a)^5}{180n^4}

    where

    \left| f^{(4)}(x)\right| \le K.

    If f is cubic the the error is zero.
    Last edited by Jester; January 28th 2009 at 09:04 AM.
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