ap calculus february 17, 2009

Download AP Calculus February 17, 2009

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  • 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