# 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

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