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# Annotation of /branches/CMA/set8.5_Representation_of_Periodic_Functions/jdl702.pg

 1 : david smit 1998 ## DESCRIPTION 2 : ## Abstract Definite Integral 3 : ## ENDDESCRIPTION 4 : 5 : ## KEYWORDS('Definite', 'Integral') 6 : ## Tagged by nhamblet 7 : 8 : ## DBsubject('Calculus') 9 : ## DBchapter('Integrals') 10 : ## DBsection('The Definite Integral') 11 : ## Date('') 12 : ## Author('') 13 : ## Institution('OSU') 14 : ## TitleText1('') 15 : ## EditionText1('') 16 : ## AuthorText1('') 17 : ## Section1('') 18 : ## Problem1('') 19 : 20 : 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 : ); 29 : 30 : TEXT(beginproblem()); 31 : $showPartialCorrectAnswers = 1; 32 : 33 :$a= random(-10, 10, 1); 34 : $a1 = random(1, 10, 1); 35 :$a2 = random(1, 10, 1); 36 : $a3 = random(1, 10, 1); 37 :$b1 = random(1,3,.5); 38 : $b =$a+$b1; 39 :$c = $b+$b1; 40 : $d =$c+$b1; 41 : 42 : BEGIN_TEXT 43 : Let $$\int_{a}^{d} f(x) dx =a1, \int_{a}^{b} f(x) dx=a2, 44 : \int_{c}^{d} f(x)dx =a3$$. 45 :$BR 46 : Find $$\int_{b}^{c} f(x)dx=$$ \{ans_rule( 10)\} 47 : $BR and $$\int_{c}^{b} (a1 f(x)- a2)dx=$$ \{ans_rule( 10)\} 48 :$PAR 49 : END_TEXT 50 : 51 : $ans1=$a1-$a2-$a3; 52 : $ans2=-$a1*$ans1+$a2*$b1; 53 : 54 : ANS(num_cmp($ans1), num_cmp(\$ans2)); 55 : 56 : BEGIN_TEXT 57 : This is similar to Problems 9-12 in Section 5.3 of the text. 58 : END_TEXT 59 : ENDDOCUMENT(); # This should be the last executable line in the problem. 60 :