This document discusses numerical integration techniques for approximating integrals. It introduces left- and right-hand sums, trapezoid sums, and midpoint sums as methods for approximating integrals when an exact antiderivative cannot be found. It then provides a table for using these summation methods with increasing values of n to calculate an integral, observe the resulting errors, and determine if there is a pattern in how the error sizes decrease.

1. How important is it to know
what quot;approximatequot; means?
or
quot;How I learned to stop
worrying and love Numerical
Integration.quot;

2. Now find each of these antiderivatives ...

3. How do you find an integral when you can't find an antiderivative?

4. Left- and Right-Hand Sums

5. Trapezoid Sums

6. Midpoint Sums

7. 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