## DESCRIPTION
## Calculus
## ENDDESCRIPTION

## KEYWORDS('calculus','integration','fundamental theorem of calculus')
## Tagged by cmd6a 8/9/06

## DBsubject('Calculus')
## DBchapter('Integrals')
## DBsection('The Fundamental Theorem of Calculus')
## Date('8/23/07')
## Author('K. Lesh')
## Institution('Union College')
## TitleText1('Calculus')
## EditionText1('7')
## AuthorText1('Anton')
## Section1('6.6')
## Problem1('4')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
  "PGstandard.pl",
  "PGunion.pl",            # Union College utilities
  "MathObjects.pl",
  "PGcourse.pl",           # Customization file for the course
);

TEXT(beginproblem());

###################################
# Setup

$lower =-1;                     # left endpoint of the interval of integration
$upper = 1;                     # right endpoint of the interval of integration
$c = non_zero_random(2,5,1);

$integrand = Formula("{$c} / {x^2+1}")->reduce;

###################################
# Main text

Context()->texStrings;
BEGIN_TEXT
Use the Fundamental Theorem of Calculus to evaluate the definite integral.
$PAR
\( \displaystyle\int_{$lower}^{\,$upper} $integrand \,dx \)
             = \{ans_rule(50)\}
END_TEXT
Context()->normalStrings;

###################################
# Answers

$showPartialCorrectAnswers = 1;

$antideriv=Formula("$c tan^(-1)(x)");
$ftc=$antideriv->eval(x=>$upper) - $antideriv->eval(x=>$lower);

ANS(Compute("$c/2 *pi")->cmp);  ## Using this to display pi in answer rather than usual ANS below
#ANS(Real($ftc)->cmp);

###################################


COMMENT('MathObject version');
ENDDOCUMENT();