##KEYWORDS('integrals', 'integration by parts')
##DESCRIPTION
## Use integration by parts to evaluate a definite integral.
##ENDDESCRIPTION

## AmberHolden tagged
## Shotwell cleaned

## DBsubject('Calculus')
## DBchapter('Techniques of Integration')
## DBsection('Integration by Parts')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('7.1')
## Problem1('17,18')


DOCUMENT();

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

$showPartialCorrectAnswers = 1;

$a = random(2,9,1);
$ans = "2/3 * $a^(3/2) * ln($a) - 4/9 * ($a^(3/2) - 1)";

TEXT(beginproblem());

BEGIN_TEXT
Use integration by parts to evaluate the definite integral.
$BR$BR 
\[ \int_{1}^{$a} \sqrt{t} \ln t dt \]
$BR 
Answer: \{ans_rule( 60) \}
END_TEXT

##set $PG_environment{'textbook'} in webworkCourse.ph
if (defined($textbook)) {
   if ($textbook eq "EllisGulick5") {
BEGIN_TEXT
$PAR
This is similar to problem 32 of section 7.1 of the text.
END_TEXT
}
}

ANS(num_cmp($ans));

ENDDOCUMENT();
________________________________________________________________________________

##DESCRIPTION
##KEYWORDS('integrals', 'integration by parts')
##Use integration by parts to evaluate the integral
##ENDDESCRIPTION

## BenBush tagged and PAID on 2-20-2004

## DBsubject('Calculus')
## DBchapter('Techniques of Integration')
## DBsection('Integration by Parts')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('7.1')
## Problem1('3,10,11,12,15,16,28,30,32,35,36,42,46')

DOCUMENT();

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

$showPartialCorrectAnswers = 1;

$a = random(1,7,1);
$e = exp(1);
$ans = - $a * $e**(- $a) - $e**(- $a) + 1;

TEXT(beginproblem());

BEGIN_TEXT
Evaluate the definite integral.
$BR \[ \int_{0}^{$a} t e^{-t} dt \]
$BR $BR \{ans_rule( 60) \}
END_TEXT

##set $PG_environment{'textbook'} in webworkCourse.ph
if (defined($textbook)) {
   if ($textbook eq "EllisGulick5") {
BEGIN_TEXT
$PAR
This is similar to problem 29 in section 7.1 of the text.
END_TEXT
}
}

ANS(num_cmp($ans));

ENDDOCUMENT();
________________________________________________________________________________

## DESCRIPTION
## Calculus: Integration by Parts
## ENDDESCRIPTION

## KEYWORDS('calculus', 'integrals', 'integration by parts')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Techniques of Integration')
## DBsection('Integration by Parts')
## Date('6/6/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('7.1')
## Problem1('6')

## Before doing anything, we must import the macro definitions on the next few lines.

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

$ans = "($a/$b)*(1-($b*x)**2)**(1/2) + $a*x*arcsin($b*x)";

TEXT(EV2(<<EOT));

Evaluate the indefinite integral.
$BR \[ \int $a \sin^{-1} ( $b x ) \; dx \]
$BR $BR 
Answer = \{ans_rule(60) \}
$BR
EOT


ANS(fun_cmp($ans, limits=>[0,.15], mode=>"antider", vars=>"x"));

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

## DESCRIPTION
## Calculus: Integration by Parts
## ENDDESCRIPTION

## KEYWORDS('calculus', 'integrals', 'integration by parts')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Techniques of Integration')
## DBsection('Integration by Parts')
## Date('6/6/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('7.1')
## Problem1('5')

## Before doing anything, we must import the macro definitions on the next few lines.

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 = 1;

$a = random(2,9,1)*random(-1,1,2);
$b = random(2,5,1)*random(-1,1,2);
$funct = "($a/($b)**2) * (-($b*x)*cos($b*x) + sin($b*x))";

TEXT(EV2(<<EOT));

Evaluate the integral.
$BR \[ \int $a x \sin ($b x) \; dx \]
$BR $BR
Answer =  \{ans_rule(60) \}
$BR
EOT

$ans = $funct;
ANS(fun_cmp($ans, mode=>"antider"));

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

## DESCRIPTION
## Calculus: Integration by Parts
## ENDDESCRIPTION

## KEYWORDS('calculus', 'integrals', 'integration by parts')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Techniques of Integration')
## DBsection('Integration by Parts')
## Date('6/6/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('7.1')
## Problem1('1')


## Before doing anything, we must import the macro definitions on the next few lines.

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 = 1;

$a = random(2,9,1)*random(-1,1,2);
$b = random(2,5,1);
$e = exp(1);
$soln = ($a/(1+$b)**2)*(1+$b*$e**(1+$b));

TEXT(EV2(<<EOT));
Evaluate the definite integral.
$BR \[ \int_{1}^{e} $a t^{$b} \ln(t) \; dt \]
$BR $BR 
Answer = \{ans_rule(40) \}
$BR
EOT

ANS(num_cmp($soln));

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

## DESCRIPTION
## Calculus: Integration by Parts
## ENDDESCRIPTION

## KEYWORDS('calculus', 'integrals', 'integration by parts')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Techniques of Integration')
## DBsection('Integration by Parts')
## Date('6/6/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('7.1')
## Problem1('10')

## Before doing anything, we must import the macro definitions on the next few lines.

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 = 1;

$a = random(2,9,1)*random(-1,1,2);
$k = random(2,5,1)*random(-1,1,2);
$e = exp(1);
$soln = ($a/$k**3)*(-2 + 2*$e**$k - 2*$k*$e**$k + ($k**2)*$e**$k);
# $soln = ($a/$k**2)*($e**$k*($k-1)-1);

TEXT(EV2(<<EOT));
Evaluate the definite integral.
$BR \[ \int_{0}^{1} $a x^2 e^{$k x} \; dx \]
$BR $BR 
Answer = \{ans_rule(40) \}
$BR
EOT

ANS(num_cmp($soln));

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

## DESCRIPTION
## Calculus: Integration by Parts
## ENDDESCRIPTION

## KEYWORDS('calculus', 'integrals', 'integration by parts')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Techniques of Integration')
## DBsection('Integration by Parts')
## Date('6/6/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('7.1')
## Problem1('1')

DOCUMENT();

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

$showPartialCorrectAnswers = 1;

$a=random(2, 7);
$ans = "x*(ln($a*x))^2 - 2*x*ln($a *x) + 2*x";

TEXT(beginproblem());

BEGIN_TEXT
Evaluate the integral.
$BR \[ \int (\ln ($a x))^2 \; dx \]
$BR $BR \{ans_rule(50) \}  \(+C\)
END_TEXT

##set $PG_environment{'textbook'} in webworkCourse.ph
if (defined($textbook)) {
   if ($textbook eq "EllisGulick5") {
BEGIN_TEXT
$PAR
This is similar to problem 5 of section 7.1 of the text.
END_TEXT
}
}

ANS(fun_cmp($ans, mode=>"antider"));

ENDDOCUMENT();
________________________________________________________________________________

## DESCRIPTION
## Calculus: Integration by Parts
## ENDDESCRIPTION

## KEYWORDS('calculus', 'integrals', 'integration by parts')
## Tagged by XW

## DBsubject('Calculus')
## DBchapter('Techniques of Integration')
## DBsection('Integration by Parts')
## Date('6/6/2005')
## Author('Jeff Holt')
## Institution('UVA')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('7.1')
## Problem1('11')

## Before doing anything, we must import the macro definitions on the next few lines.

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

$d = $a**2 + $b**2;

$ans = "- $b/$d * (e^($a*x) * cos($b*x)) + $a/$d * (e^($a*x) * sin($b*x))";

TEXT(EV2(<<EOT));

Evaluate the indefinite integral.
$BR \[ \int e^{$a x} \sin ( $b x ) \; dx \]
$BR $BR 
Answer = \{ans_rule(60) \}
$BR
EOT


ANS(fun_cmp($ans, mode=>"antider"));

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

##KEYWORDS('integrals', 'integration by parts', 'substitution method')
##DESCRIPTION
## Evaluate integral using substitution and integration by parts
##ENDDESCRIPTION

## AmberHolden tagged
## Shotwell cleaned

## DBsubject('Calculus')
## DBchapter('Techniques of Integration')
## DBsection('Integration by Parts')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('7.1')
## Problem1('31')

DOCUMENT();

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

$showPartialCorrectAnswers = 1;

$a=random(2, 7);
$expnt = -1+2*$a;
$ans = "1/$a * x^$a * sin(x^$a) + 1/$a * cos(x^$a)";

TEXT(beginproblem());

BEGIN_TEXT
First make a substitution and then use integration by parts to evaluate the
integral.
$BR \[ \int x^{$expnt} \cos (x^$a) dx \] $BR
 Answer: \{ans_rule(40) \}  \(+\) \(C\)
END_TEXT

##set $PG_environment{'textbook'} in webworkCourse.ph
if (defined($textbook)) {
   if ($textbook eq "EllisGulick5") {
BEGIN_TEXT
This is similar to problem 38 in section 7.1 of the text.
END_TEXT
}
}

ANS(fun_cmp($ans, mode=>'antider'));

ENDDOCUMENT();
________________________________________________________________________________

##KEYWORDS('integrals', 'integration by parts')
##DESCRIPTION
## Use integration by parts to evaluate an indefinite integral
##ENDDESCRIPTION

## AmberHolden tagged
## Shotwell cleaned

## DBsubject('Calculus')
## DBchapter('Techniques of Integration')
## DBsection('Integration by Parts')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('7.1')
## Problem1('2')



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

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

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

$a = random(2,9,1);
$soln = "x*tan($a*x)/$a-ln(abs(sec($a*x)))/$a^2";

BEGIN_TEXT
Use integration by parts to evaluate the indefinite integral.
$BR$BR 
\[ \int  x \sec^2 ($a x) dx \]
$BR 
Answer: \{ans_rule(40) \} \(+\) \(C\)
$BR
END_TEXT

ANS(fun_cmp($soln, mode=>'antider'));

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