[npl] / trunk / NationalProblemLibrary / Rochester / setIntegrals0Theory / osu_in_0_14.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

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

Fri May 28 14:52:41 2010 UTC (3 years ago) by gage
File size: 1473 byte(s)
updates to show problem source for model_Calculus_1


    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
29 "PG.pl",
30 "PGbasicmacros.pl",
31 "PGchoicemacros.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