View of /trunk/NationalProblemLibrary/Rochester/setIntegrals19Area/osu_in_19_15.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('integration','graph','area')
    6 ## Tagged by cmd6a 4/26/06
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Integration')
   10 ## DBsection('Areas Between Curves')
   11 ## Date('1/19/2000')
   12 ## Author('Zig Fiedorowicz')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 ## TitleText2('Calculus: Early Transcendentals')
   20 ## EditionText2('1')
   21 ## AuthorText2('Rogawski')
   22 ## Section2('6.1')
   23 ## Problem2('19')
   24 
   25 DOCUMENT();
   26 
   27 loadMacros(
   28 "PG.pl",
   29 "PGbasicmacros.pl",
   30 "PGchoicemacros.pl",
   31 "PGanswermacros.pl",
   32 "PGauxiliaryFunctions.pl"
   33 );
   34 
   35 $showPartialCorrectAnswers = 1;
   36 
   37 $a = random(1,5,1);
   38 $a1 = random(1,3,1);
   39 $c = $a +$a1;
   40 $lin =  -$a*$c;
   41 $quadr = $a+$c;
   42 $eva = $quadr*$a**3/3-$a**4/4+$lin*$a**2/2;
   43 $evc = $quadr*$c**3/3-$c**4/4+$lin*$c**2/2;
   44 $answ = abs($eva)+abs($evc-$eva);
   45 $c2 = $quadr +1;
   46 $c1 = -$lin+1;
   47 
   48 TEXT(beginproblem());
   49 BEGIN_TEXT
   50 The total area enclosed by the graphs of
   51 \[y = $c2 x^2 - x^3 + x\]
   52 \[y = x^2 + $c1 x\]
   53 is \{ ans_rule()\}
   54 END_TEXT
   55 
   56 ANS(num_cmp($answ));
   57 
   58 ENDDOCUMENT();
   59