Download - AP Calculus February 17, 2009
Transcript
Numeric Integrationor How Close is Close Enough?
Near Miss by flickr user The Rocketeer
Left- and Right-Hand Sums
Trapezoid Sums
Midpoint Sums
n M (midpoint sum) Error T (trapezoid sum) Error
4
8
16
n n
Use your calculator and the RIESUM program to complete the table for this integral.Is there a pattern in the error sizes?
HOMEWORK
Error Estimates for Trapezoid and Midpoint Sums
Trapezoid Sums
Midpoint Sums
a & b are endpoints of an intervaln is the number of subdivisions
M is the maximum value of the second derivative on the given interval.2
Simpson Sums
S = 2M + Tn n n3
http://www.math.duke.edu/education/ccp/materials/intcalc/numint/contents.html
Numeric Computation of Integrals
You can find a nice review of today's lesson here:
http://tinyurl.com/bg5345