##DESCRIPTION #KEYWORDS('integrals', 'trigonometry','substitution') ## use trig identities, then substitute. ##ENDDESCRIPTION DOCUMENT(); # This should be the first executable line in the problem. ## BenBush tagged and PAID on 2-20-2004 ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Trigonometric Integrals') ## Date('6/3/2002') ## Author('') ## Institution('') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('7.2') ## Problem1('1,2,5,18') loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$n = random(4,20,2); $ans = 1/($n + 1) - 2/($n + 3) + 1/($n + 5); TEXT(EV2(<"antider")); ENDDOCUMENT(); # This should be the last executable line in the problem. ________________________________________________________________________________ ##KEYWORDS('integrals', 'trigonometric') ##DESCRIPTION ## Evaluate an integral ##ENDDESCRIPTION ## AmberHolden tagged ## Shotwell cleaned ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Trigonometric Integrals') ## Date('6/3/2002') ## Author('') ## Institution('') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('7.2') ## Problem1('1,2,5') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PGbasicmacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$l = random(3,10,1); $a = random(2,20,1);$l1 = $l+1;$l3 = $l+3;$funct = "-cos($a * x)^($l1)/($l1 *$a)+ cos($a * x)^($l3)/($l3 *$a)"; BEGIN_TEXT Evaluate the indefinite integral. $BR $\int \sin^3(a x)\cos^{l}(a x) dx$$BR Answer: \{ans_rule( 60) \} $$+$$ $$C$$ $BR END_TEXT ANS(fun_cmp($funct, mode=>'antider')); ENDDOCUMENT(); # This should be the last executable line in the problem. ________________________________________________________________________________ ##DESCRIPTION ##KEYWORDS('integrals', 'trig', 'half angle identity', 'substitution') ## Use half angle identity and substitution ##ENDDESCRIPTION ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Trigonometric Integrals') ## Date('6/3/2002') ## Author('') ## Institution('') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('7.2') ## Problem1('13,14,48') 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;$c = random(2,9,1); $a = random(0,8,1);$len = random(3,10,1); $b=$a + $len;$ans = $len/8 - (sin(4*$b*$c) - sin(4*$a*$c))/(32*$c); TEXT(EV2(<"antider")); ENDDOCUMENT(); ________________________________________________________________________________ ##DESCRIPTION ##KEYWORDS('integrals', 'trigonometry', 'substitution') ## use trig identities, then substitute. ##ENDDESCRIPTION ## BenBush tagged and PAID on 2-20-2004 ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Trigonometric Integrals') ## Date('6/3/2002') ## Author('') ## Institution('') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('7.2') ## Problem1('25,26,27,28,29,30,33,34,37,38,45') 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;$l = random(2,15,1); $a = random(2,20,1);$a3 = 3*$a;$soln = (2**$l -1)/($l*$a); TEXT(EV2(<'antider', limits=>[[-2,2]])); ENDDOCUMENT(); # This should be the last executable line in the problem. ________________________________________________________________________________ ##KEYWORDS('integrals', 'trig') ##DESCRIPTION ## Evaluate the integral ##ENDDESCRIPTION ## AmberHolden tagged ## Shotwell cleaned ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Trigonometric Integrals') ## Date('6/3/2002') ## Author('') ## Institution('') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('7.2') ## Problem1('25,26') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PGbasicmacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem());$showPartialCorrectAnswers = 1; $a = random(4,9,1);$funct = "(tan(x))^($a+1)/($a+1)"; BEGIN_TEXT Evaluate the indefinite integral. $BR $\int \tan^{a} x \sec^2 x \,dx$$BR Answer: \{ans_rule( 45) \} $$+ C$$ $BR END_TEXT ANS(fun_cmp($funct, mode=>'antider')); ENDDOCUMENT(); # This should be the last executable line in the problem. ________________________________________________________________________________ ##KEYWORDS('integrals', 'trig') ##DESCRIPTION ## Evaluate an indefinite integral ##ENDDESCRIPTION ## AmberHolden tagged ## Shotwell cleaned ## DBsubject('Calculus') ## DBchapter('Techniques of Integration') ## DBsection('Trigonometric Integrals') ## Date('6/3/2002') ## Author('') ## Institution('') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('7.2') ## Problem1('27,28,29') 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); $funct = "-(-(cos($a*x))^(-3)/3+1/cos($a*x))/$a"; BEGIN_TEXT Evaluate the indefinite integral. $BR $\int \tan^3 (a x) \sec (a x) \,dx$$BR Answer: \{ans_rule( 45) \} $$+ C$$ $BR END_TEXT ANS(fun_cmp($funct, mode=>'antider')); ENDDOCUMENT(); # This should be the last executable line in the problem. ________________________________________________________________________________ ##DESCRIPTION #KEYWORDS('integrals', 'trigonometry','substitution') ## use trig identities, then substitution ##ENDDESCRIPTION ## BenBush tagged and PAID on 2-20-2004 ## DBchapter('Techniques of Integration') ## DBsection('Trigonometric Integrals') ## Date('6/3/2002') ## Author('Tangan Gao') ## Institution('csulb') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('7.2') ## Problem1('26') 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(3,9,1); $b = random(3,6,1);$c = $a*$b; $p = arccos(-1);$t = tan($p/$b); $soln =$t*$t*$t*$t*$t*$t*$t/($a*7)+$t*$t*$t*$t*$t/($a*5); BEGIN_TEXT Evaluate the definite integral.$BR $\int_{0}^{\frac{\pi}{c}} \tan^4(a x) \sec^4(a x) dx$ $BR$BR \{ans_rule( 30) \} $BR END_TEXT$ans = $soln; &ANS(std_num_cmp($ans)); ##set \$PG_environment{'textbook'} in webworkCourse.ph ENDDOCUMENT(); # This should be the last executable line in the problem.