##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(<[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($b*x))"; TEXT(EV2(<"antider")); ENDDOCUMENT(); # This should be the last executable line in the problem. ________________________________________________________________________________ ## DESCRIPTION ## Calculus: Integration by Parts ## ENDDESCRIPTION ## KEYWORDS('calculus', 'integrals', 'integration by parts') ## Tagged by XW ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Integration by Parts') ## Date('6/6/2005') ## Author('Jeff Holt') ## Institution('UVA') ## TitleText1('Calculus') ## EditionText1('5e') ## AuthorText1('Stewart') ## Section1('7.1') ## Problem1('1') ## Before doing anything, we must import the macro definitions on the next few lines. DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem());$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+$b)); TEXT(EV2(<"antider")); ENDDOCUMENT(); ________________________________________________________________________________ ## DESCRIPTION ## Calculus: Integration by Parts ## ENDDESCRIPTION ## KEYWORDS('calculus', 'integrals', 'integration by parts') ## Tagged by XW ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Integration by Parts') ## Date('6/6/2005') ## Author('Jeff Holt') ## Institution('UVA') ## TitleText1('Calculus') ## EditionText1('5e') ## AuthorText1('Stewart') ## Section1('7.1') ## Problem1('11') ## Before doing anything, we must import the macro definitions on the next few lines. DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem());$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(<"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.