October 2nd, 2011, 08:49 PM  #1 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  Simpson's Rule approximation
How large should n be to guarantee that the Simpson's Rule approximation to is accurate to within 0.0001? 
October 2nd, 2011, 10:16 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Simpson's Rule approximation
My old calculus text states concerning the error bound for Simpson's Rule: If there exists a number M > 0 such that for all x in [a,b] then So, for we compute: Analysis of shows that is increasing on (0,1] thus we find: Thus: Since n must be even we find the minimum value of n is 26. 
October 2nd, 2011, 10:55 PM  #3 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  Re: Simpson's Rule approximation
some how it worked out the be 22

October 2nd, 2011, 11:08 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Simpson's Rule approximation
Maybe I should have used: Then n would be 22. 

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