This document discusses numerical integration techniques for approximating integrals, including left- and right-hand sums, midpoint sums, and trapezoid sums. It explains that midpoint sums and trapezoid sums reduce the error of approximations and provides formulas for estimating the error bounds of these methods based on the second derivative of the function. The document also includes questions about selecting the number of subintervals needed to achieve a given error tolerance using trapezoid or midpoint sums.

1. Numerical Integration
How do you find an integral when you
can't find an integral?

2. Left- and Right-Hand 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?
(midpoint sum) Error (trapezoid sum) Error

6. Error Estimates for Trapezoid and Midpoint Sums
the maximum value of the second derivative on the given interval.
Midpoint Sums

7. In order to approximate the integral below with greatest possible error of
0.0001, how large must be if you use a:
(a) trapezoid sum? (b) midpoint sum?

9. Numeric Computation of Integrals
http://www.math.duke.edu/education/ccp/materials/intcalc/numint/contents.html