## DESCRIPTION
## Calculus: Indefinite Integrals and the Net Change Theorem
## ENDDESCRIPTION

## KEYWORDS('calculus', 'indefinite integrals', 'net change theorem')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Integrals')
## DBsection('Indefinite Integrals and the Net Change Theorem')
## Date('6/3/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('5.4')
## Problem1('7')


DOCUMENT();

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

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

$a = random(3,8,1);
$b = random(3,6,1);
$c = random(3,6,1);

TEXT(EV2(<<EOT));

Evaluate the indefinite integral:
$BR
$PAR
   \( \displaystyle{ \int \left($a x^2 + $b x - $c\right) \,dx} = \)
   \{ans_rule(35) \} + \( C\).
$BR
$BR

EOT

$ans = "($a/3)*x**3 + ($b/2)*x**2 - $c*x";
ANS(fun_cmp($ans, mode=>"antider", vars=>"x"));

ENDDOCUMENT();
________________________________________________________________________________

## DESCRIPTION
## Calculus: Indefinite Integrals and the Net Change Theorem
## ENDDESCRIPTION

## KEYWORDS('calculus', 'indefinite integrals', 'net change theorem')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Integrals')
## DBsection('Indefinite Integrals and the Net Change Theorem')
## Date('6/3/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('5.4')
## Problem1('10')

DOCUMENT();

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

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

$a = random(3,8,1);
$b = random(3,6,1);
$p = random(3,6,1);

TEXT(EV2(<<EOT));

Evaluate the indefinite integral:
$BR
$PAR
   \( \displaystyle{ \int \left(x^{$p} + $a + \frac{$b}{x^{2}+1}\right) \,dx} = \)
   \{ans_rule(35) \} + \( C\).
$BR
$BR

EOT

$ans = "x**($p+1)/($p+1)+$a*x+$b*arctan(x)";
ANS(fun_cmp($ans, mode=>"antider", vars=>"x"));

ENDDOCUMENT();
________________________________________________________________________________

## DESCRIPTION
## Calculus: Indefinite Integrals and the Net Change Theorem
## ENDDESCRIPTION

## KEYWORDS('calculus', 'indefinite integrals', 'net change theorem')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Integrals')
## DBsection('Indefinite Integrals and the Net Change Theorem')
## Date('6/3/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('5.4')
## Problem1('12')

DOCUMENT();

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

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

$a = random(3,8,1);
$b = random(3,6,1);
$p = random(3,6,1);

TEXT(EV2(<<EOT));

Evaluate the indefinite integral:
$BR
$PAR
   \( \displaystyle{ \int \left($a e^{u} + $b \sec^2 u \right) \,du} = \)
   \{ans_rule(35) \} + \( C\).
$BR
$BR

EOT

@ans = (fun_cmp("$a*exp(u)+$b*tan(u)", mode=>"antider", vars=>"u"));
ANS(@ans);

ENDDOCUMENT();
________________________________________________________________________________

## DESCRIPTION
## Calculus: Indefinite Integrals and the Net Change Theorem
## ENDDESCRIPTION

## KEYWORDS('calculus', 'indefinite integrals', 'net change theorem')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Integrals')
## DBsection('Indefinite Integrals and the Net Change Theorem')
## Date('6/3/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('5.4')
## Problem1('14')

DOCUMENT();

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

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

$a = random(3,11,2);
$b = random(2,10,2);
$p = random(3,6,1);

TEXT(EV2(<<EOT));

Evaluate the indefinite integral:
$BR
$PAR
   \( \displaystyle{ \int \frac{$a \sin 2x}{$b \sin x} \,dx} = \)
   \{ans_rule(35) \} + \( C\).
$BR
$BR

EOT

@ans = (fun_cmp("(2*$a/$b)*sin(x)", mode=>"antider", vars=>"x"));
ANS(@ans);

ENDDOCUMENT();
________________________________________________________________________________

## DESCRIPTION
## Calculus: Indefinite Integrals and the Net Change Theorem
## ENDDESCRIPTION

## KEYWORDS('calculus', 'indefinite integrals', 'net change theorem')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Integrals')
## DBsection('Indefinite Integrals and the Net Change Theorem')
## Date('6/3/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('5.4')
## Problem1('19')

DOCUMENT();

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

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

$a = random(2,6,1);
$b = random(2,6,1);
$c = random(2,6,1);

TEXT(EV2(<<EOT));

Evaluate the definite integral:
$BR
$PAR
   \( \displaystyle{ \int_{-$a}^{$b} \left($c x - e^x\right) \,dx} = \)
   \{ans_rule(35) \}
$BR
$BR

EOT

$ans = $c*($b**2-$a**2)/2-(exp($b)-exp(-$a));
ANS(num_cmp($ans));

ENDDOCUMENT();
________________________________________________________________________________

## DESCRIPTION
## Calculus: Indefinite Integrals and the Net Change Theorem
## ENDDESCRIPTION

## KEYWORDS('calculus', 'indefinite integrals', 'net change theorem')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Integrals')
## DBsection('Indefinite Integrals and the Net Change Theorem')
## Date('6/3/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('5.4')
## Problem1('21')

DOCUMENT();

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

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

$a = random(-8,-5,1);
$b = random(-4,-1,1);
$c = random(2,5,1);

TEXT(EV2(<<EOT));

Evaluate the definite integral:
$BR
$PAR
   \( \displaystyle{ \int_{$a}^{$b} \left(-$c x^{-2} + x^{-1}\right) \,dx} = \)
   \{ans_rule(35) \}
$BR
$BR

EOT

$ans = ($c)*(1/$b - 1/$a) + ln(abs($b)) - ln(abs($a));
ANS(num_cmp($ans));

ENDDOCUMENT();
________________________________________________________________________________

## DESCRIPTION
## Calculus: Indefinite Integrals and the Net Change Theorem
## ENDDESCRIPTION

## KEYWORDS('calculus', 'indefinite integrals', 'net change theorem')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Integrals')
## DBsection('Indefinite Integrals and the Net Change Theorem')
## Date('6/3/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('5.4')
## Problem1('25')

DOCUMENT();

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

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

$p = random(1,5,1);
$p1 = random(2,4,1);
$p2 = $p1+$p;



TEXT(EV2(<<EOT));

Evaluate the definite integral:
$BR
$PAR
   \( \displaystyle{ \int_{0}^{1} u(\sqrt[$p1]{u}+\sqrt[$p2]{u}) \,du} = \)
   \{ans_rule(45) \} 
$BR
$BR

EOT

$ans = $p1/(2*$p1+1)+$p2/(2*$p2+1);
ANS(num_cmp($ans));

ENDDOCUMENT();
________________________________________________________________________________

## DESCRIPTION
## Calculus: Indefinite Integrals and the Net Change Theorem
## ENDDESCRIPTION

## KEYWORDS('calculus', 'indefinite integrals', 'net change theorem')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Integrals')
## DBsection('Indefinite Integrals and the Net Change Theorem')
## Date('6/3/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('5.4')
## Problem1('27')


DOCUMENT();

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

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

$a = random(1,4,1);
$b = random(12,26,1);
$c = random(2,6,1);

TEXT(EV2(<<EOT));

Evaluate the definite integral:
$BR
$PAR
   \( \displaystyle{ \int_{$a}^{$b} \frac{$c}{ \sqrt{x}} \,dx} = \)
   \{ans_rule(35) \}
$BR
$BR

EOT

$ans = (2*$c)*($b**(1/2) - $a**(1/2));
ANS(num_cmp($ans));

ENDDOCUMENT();
________________________________________________________________________________

## DESCRIPTION
## Calculus: Indefinite Integrals and the Net Change Theorem
## ENDDESCRIPTION

## KEYWORDS('calculus', 'indefinite integrals', 'net change theorem')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Integrals')
## DBsection('Indefinite Integrals and the Net Change Theorem')
## Date('6/3/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('5.4')
## Problem1('57')

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

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

TEXT(beginproblem());
$showPartialCorrectAnswers = 0;

$a = random(2,7,1);
$b1 = random(2,5,1);
$b = $b1*5;

$c = random(2,4,1);
$l = $c**2;


TEXT(EV2(<<EOT));
The linear density of a rod of length $l m is given by
\[ \rho(x) = $a + $b \sqrt{x} \]

measured in kilograms per meter, where \( x \) is measured in meters
 from one end of the rod.  Find the total mass of the rod.

$PAR
Total mass = \{ans_rule(30) \}
$PAR
EOT

$ans1 = $a*$l+(2/3)*$b*$l**(3/2);

ANS(num_cmp($ans1));

ENDDOCUMENT();
________________________________________________________________________________

## DESCRIPTION
## Calculus: Indefinite Integrals and the Net Change Theorem
## ENDDESCRIPTION

## KEYWORDS('calculus', 'indefinite integrals', 'net change theorem')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Integrals')
## DBsection('Indefinite Integrals and the Net Change Theorem')
## Date('6/3/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('5.4')
## Problem1('58')

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

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

TEXT(beginproblem());
$showPartialCorrectAnswers = 0;

$a = random(100,900,100);
$b = random(10,90,10);


$n = random(1,9,1);
$d = random(2,6,1);
$m = $n+$d;


TEXT(EV2(<<EOT));
A population of cattle is increasing at a rate of \( $a + $b \, t \) 
per year, where \( t \) is measured in years.  By how much does the population 
increase between the $n th and the $m th years.

$PAR
Total Increase = \{ans_rule(30) \}
$PAR
EOT

$ans1 = $a*($m-$n)+$b/2*($m**2-$n**2);

ANS(num_cmp($ans1));

ENDDOCUMENT();