Accuracy with numerical integration.

1. Numeric Integration
or How Close is Close Enough?
Near Miss by flickr user The Rocketeer

2. Left- and Right-Hand Sums

3. Trapezoid Sums

4. Midpoint 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