View of /trunk/NationalProblemLibrary/Rochester/setIntegrals0Theory/osu_in_0_14.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('integral' 'summation' 'area')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Integrals')
   10 ## DBsection('Area and Distance')
   11 ## Date('')
   12 ## Author('')
   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('5.2')
   23 ## Problem2('1')
   24 
   25 
   26 DOCUMENT();
   27 
   28 loadMacros(
   29 "PG.pl",
   30 "PGbasicmacros.pl",
   31 "PGchoicemacros.pl",
   32 "PGanswermacros.pl",
   33 "PGauxiliaryFunctions.pl",
   34 "PGcourse.pl"
   35 );
   36 
   37 $showPartialCorrectAnswers = 1;
   38 
   39 $x[0] = random(-8,8,1);
   40 $y[0] = random(-1,1,2)*random(1,8,1);
   41 
   42 $area = 0;
   43 
   44 for ($i=1; $i<4; $i++) {
   45     $x[$i] = $x[$i-1] + random(2,5,1);
   46     $y[$i] = random(1,8,1);
   47     if ($y[$i-1]>0) {$y[$i] = - $y[$i];}
   48     $area = $area + ($y[$i-1]+$y[$i])*($x[$i]-$x[$i-1])/2;
   49 }
   50 
   51 TEXT(beginproblem());
   52 
   53 BEGIN_TEXT
   54 You are given the four points in the plane \(A = ($x[0],$y[0])\),
   55 \(B = ($x[1],$y[1])\),  \(C = ($x[2],$y[2])\), and \(D = ($x[3],$y[3])\).
   56 The graph of the function \(f(x)\) consists of the three line segments
   57 \(AB\), \(BC\) and \(CD\).  Find the integral \( \displaystyle \int_{$x[0]}^{$x[3]} f(x)\,dx\)
   58 by interpreting the integral in terms of sums and/or differences of areas of
   59 elementary figures.
   60 $BR
   61 \( \displaystyle \int_{$x[0]}^{$x[3]} f(x)\,dx =\) \{ans_rule()\}
   62 END_TEXT
   63 
   64 ANS(num_cmp($area));
   65 
   66 ENDDOCUMENT();
   67