View of /trunk/NationalProblemLibrary/ma122DB/set11/s5_2_45.pg

    1 ##DESCRIPTION
    2 ##  Write a difference of two integrals as a single integral
    3 ##This is setIntegrals0Theory/nttheo1.pg slightly cleaned up and expanded
    4 ##by Zig Fiedorowicz, Jan. 2001
    5 ##ENDDESCRIPTION
    6 ##KEYWORDS('integrals', 'theory')
    7 
    8 ## Shotwell cleaned
    9 ## lcao , PAID on 11-24-2003
   10 
   11 ## DBsubject('Calculus')
   12 ## DBchapter('Integrals')
   13 ## DBsection('The Definite Integral')
   14 ## Date('6/3/2002')
   15 ## Author('')
   16 ## Institution('')
   17 ## TitleText1('Calculus: Early Transcendentals')
   18 ## EditionText1('6')
   19 ## AuthorText1('Stewart')
   20 ## Section1('5.2')
   21 ## Problem1('46')
   22 
   23 DOCUMENT();        # This should be the first executable line in the problem.
   24 
   25 loadMacros(
   26 "PGbasicmacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl"
   29 );
   30 
   31 TEXT(beginproblem());
   32 $showPartialCorrectAnswers = 1;
   33 
   34 $a= random(-10, 10);
   35 $a1 = random(2, 10);
   36 $a2 = random(2, 10);
   37 $a3 = random(1, 10);
   38 $b1 = random(1,3,.5);
   39 $b = $a+$b1;
   40 $c = $b+$b1;
   41 $d = $c+$b1;
   42 
   43 BEGIN_TEXT
   44 Let \( \displaystyle \int_{$a}^{$d} f(x)\, dx =$a1, \ \int_{$a}^{$b} f(x)\, dx=$a2, \ \int_{$c}^{$d} f(x)\, dx =$a3 \).
   45 $BR$BR
   46 Find \( \displaystyle \int_{$b}^{$c} f(x)\, dx= \) \{ans_rule( 20)\}
   47 $BR
   48 $BR
   49 and \( \displaystyle \int_{$c}^{$b} $a1 f(x)- $a2 \, dx= \) \{ans_rule( 20)\}
   50 
   51 END_TEXT
   52 
   53 $ans1="$a1-($a2)-($a3)";
   54 $ans2="-($a1*($ans1))+$a2*$b1";
   55 
   56 ANS(num_cmp($ans1), num_cmp($ans2));
   57 
   58 ##set $PG_environment{'textbook'} in webworkCourse.ph
   59 if (defined($textbook)) {
   60    if ($textbook eq "EllisGulick5") {
   61 BEGIN_TEXT
   62 This is similar to Problems 9-12 in Section 5.3 of the text.
   63 END_TEXT
   64 }
   65 }
   66 
   67 ENDDOCUMENT();        # This should be the last executable line in the problem.
   68