AP Calculus February 17, 2009
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This document discusses numerical integration techniques for approximating definite integrals, including left- and right-hand sums, trapezoid sums, midpoint sums, and Simpson's rule. It provides a table to calculate the error in midpoint and trapezoid sums for different values of n subdivisions. It also gives error estimates for trapezoid and midpoint sums that depend on the interval endpoints a and b, the number of subdivisions n, and the maximum value of the second derivative on the interval. The document provides links for online resources that provide more information on numerical integration methods.
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- 1. Numeric Integration or How Close is Close Enough? Near Miss by flickr user The Rocketeer
- 2. Left- and Right-Hand Sums
- 5. Use your calculator and the RIESUM program to complete the table for this integral. Is there a pattern in the error sizes? HOMEWORK n Mn (midpoint sum) T (trapezoid sum) Error Error n 4 8 16
- 6. Error Estimates for Trapezoid and Midpoint Sums Trapezoid Sums a & b are endpoints of an interval n is the number of subdivisions M2 is the maximum value of the second derivative on the given interval. Midpoint Sums
- 7. Simpson Sums Sn = 2Mn + Tn 3
- 8. Numeric Computation of Integrals http://tinyurl.com/bg5345 You can find a nice review of today's lesson here: http://www.math.duke.edu/education/ccp/materials/intcalc/numint/contents.html