Thread: 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

Originally Posted by desdemoniagirl

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.

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

Originally Posted by desdemoniagirl

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 $\displaystyle E_s$ which is given by

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

where

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

If f is cubic the the error is zero.