## DESCRIPTION
## Text inserted into other problems
## ENDDESCRIPTION

## KEYWORDS()
## Tagged by jjh2b 8/22/06

## DBsubject('ZZZ-Inserted Text')
## DBchapter('ZZZ-Inserted Text')
## DBsection('ZZZ-Inserted Text')
## Date('9/15/04')
## Author('K. Lesh')
## Institution('Union College')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')


$offset = 0 unless defined $offset;
$percent = 100*$offset;
if ($offset == 0)  {$points = "left endpoints";}
     elsif ($offset == 1)  {$points = "right endpoints";}
     elsif ($offset == .5) {$points = "midpoints";}
     else  {$points = "points that are $percent $PERCENT of the way from
             left to right";}

$ans=RiemannSum($a,$b,$n,$offset);

BEGIN_TEXT
Estimate
\( \displaystyle\int_{$a}^{\,$b} $f \,dx\)
using $points for \( n = $n \) approximating rectangles.
$PAR
\( \displaystyle\int_{$a}^{\,$b} $f \,dx\) is approximately \{ans_rule(45)\}
END_TEXT