##DESCRIPTION
##  Write a difference of two integrals as a single integral
##This is setIntegrals0Theory/nttheo1.pg slightly cleaned up and expanded
##by Zig Fiedorowicz, Jan. 2001
##ENDDESCRIPTION
##KEYWORDS('integrals', 'theory')

## Shotwell cleaned
## lcao , PAID on 11-24-2003

## DBsubject('Calculus')
## DBchapter('Integrals')
## DBsection('The Definite Integral')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('5.2')
## Problem1('46')

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

loadMacros(
"PGbasicmacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$a= random(-10, 10);
$a1 = random(2, 10);
$a2 = random(2, 10);
$a3 = random(1, 10);
$b1 = random(1,3,.5);
$b = $a+$b1;
$c = $b+$b1;
$d = $c+$b1;

BEGIN_TEXT
Let \( \displaystyle \int_{$a}^{$d} f(x)\, dx =$a1, \ \int_{$a}^{$b} f(x)\, dx=$a2, \ \int_{$c}^{$d} f(x)\, dx =$a3 \). 
$BR$BR
Find \( \displaystyle \int_{$b}^{$c} f(x)\, dx= \) \{ans_rule( 20)\} 
$BR
$BR 
and \( \displaystyle \int_{$c}^{$b} $a1 f(x)- $a2 \, dx= \) \{ans_rule( 20)\}

END_TEXT

$ans1="$a1-($a2)-($a3)";
$ans2="-($a1*($ans1))+$a2*$b1";

ANS(num_cmp($ans1), num_cmp($ans2));

##set $PG_environment{'textbook'} in webworkCourse.ph
if (defined($textbook)) {
   if ($textbook eq "EllisGulick5") {
BEGIN_TEXT
This is similar to Problems 9-12 in Section 5.3 of the text.
END_TEXT
}
}

ENDDOCUMENT();        # This should be the last executable line in the problem.