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Annotation of /trunk/NationalProblemLibrary/Union/setIntBasic/an7_2_7.pg

 1 : jjholt 321 ## DESCRIPTION 2 : ## Calculus 3 : ## ENDDESCRIPTION 4 : 5 : ## KEYWORDS('calculus','integration','indefinite integral') 6 : ## Tagged by cmd6a 8/9/06 7 : 8 : ## DBsubject('Calculus') 9 : ## DBchapter('Integrals') 10 : ## DBsection('Indefinite Integrals') 11 : ## Date('9/28/03') 12 : ## Author('K. Lesh') 13 : ## Institution('Union College') 14 : ## TitleText1('') 15 : ## EditionText1('') 16 : ## AuthorText1('') 17 : ## Section1('') 18 : ## Problem1('') 19 : 20 : jj 248 DOCUMENT(); # This should be the first executable line in the problem. 21 : 22 : loadMacros( 23 : "PG.pl", 24 : "PGbasicmacros.pl", 25 : "PGchoicemacros.pl", 26 : "PGanswermacros.pl", 27 : "PGauxiliaryFunctions.pl", 28 : "PGunion.pl", # Union College utilities 29 : "PGcourse.pl", # Customization file for the course 30 : ); 31 : 32 : TEXT(beginproblem()); 33 : BEGIN_PROBLEM(); 34 : 35 : ############################################## 36 : ## problem setup: 37 : 38 : $a = random(2,8,1); 39 :$b = random(2,8,2); 40 : $c = random(5,13,2); 41 :$d = random(-6,-2,1); 42 : 43 : BEGIN_TEXT 44 : Calculate the following antiderivatives: 45 : $PAR 46 : (a) $$\displaystyle\int x^{a}\, dx$$ = \{ans_rule\} $$+ C$$. 47 :$PAR 48 : (b) $$\displaystyle\int x^{b/c} \,dx$$ = \{ans_rule\} $$+ C$$. 49 : $PAR 50 : (c) $$\displaystyle\int x^{d}\sqrt{x} \,dx$$ = \{ans_rule\} $$+ C$$. 51 : END_TEXT 52 : 53 :$showPartialCorrectAnswers = 1; 54 : ########################## 55 : 56 : $aa =$a + 1; 57 : $bb =$b + $c; 58 :$dd = $d + 1.5; 59 : ANS(fun_cmp("(1/$aa) x^($aa)", mode=>"antider")); 60 : ANS(fun_cmp("($c/$bb) x^($bb/$c)", mode=>"antider")); 61 : ANS(fun_cmp("(1/$dd) x^(\$dd)", mode=>"antider", vars=>"x", limits=>[1,2])); 62 : ############################################## 63 : 64 : END_PROBLEM(); 65 : ENDDOCUMENT(); # This should be the last executable line in the problem.