My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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?

aaron-math is offline  
 
October 2nd, 2011, 10:16 PM   #2
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 521

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.
MarkFL is offline  
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
aaron-math is offline  
October 2nd, 2011, 11:08 PM   #4
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 521

Math Focus: Calculus/ODEs
Re: Simpson's Rule approximation

Maybe I should have used:







Then n would be 22.
MarkFL is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
approximation, rule, simpson



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Simpson's Rule for a vector keresturec Calculus 1 September 17th, 2013 07:37 AM
Simpson's Rule aaron-math Calculus 1 October 2nd, 2011 10:36 PM
Simpson's Rule aaron-math Calculus 1 September 30th, 2011 04:45 AM
simpson's 1/3rd rule rakeshkool27 Calculus 4 March 21st, 2010 03:35 PM
Simpson's Rule igodspeed Calculus 1 March 3rd, 2009 11:53 PM





Copyright © 2019 My Math Forum. All rights reserved.