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# View of /trunk/rochester_problib/setIntegrals0Theory/osu_in_0_18.pg

Revision 844 - (download) (annotate)
Sun Jul 17 20:07:36 2005 UTC (7 years, 11 months ago) by gage
File size: 1117 byte(s)
Replacing std_num_cmp by num_cmp, etc. etc.  This should make
the code for our files more regular and reduce the number
of macros that need to be documented.  These macros are now
combined into one macro with various options.


    1 ##DESCRIPTION
2 ##KEYWORDS('integrals', 'inverse functions', 'area')
3 ##Find integral of inverse function
4 ##by relating it to integral of original function
5 ##via relation between areas
6 ##Authored by Zig Fiedorowicz 2/4/2000
7 ##ENDDESCRIPTION
8
9 DOCUMENT();
10
11 loadMacros(
12 "PG.pl",
13 "PGbasicmacros.pl",
14 "PGchoicemacros.pl",
15 "PGanswermacros.pl",
16 "PGauxiliaryFunctions.pl"
17 );
18 $showPartialCorrectAnswers = 1; 19 20$a= random(1,5,1);
21 $b= random(2,15,1); 22$c= random(2,10,1);
23 $quad = 3*$a;
24 $lin = 3*($a**2+$b); 25$y1 = 1 - $quad +$lin + $c; 26$y2 = 8 - $quad*4 +$lin*2 +$c; 27$a1 = 1/4 - $quad/3 +$lin/2 + $c; 28$a2 = 16/4 - $quad*8/3 +$lin*4/2 + $c*2; 29$ans = 2*$y2 -$y1 - $a2 +$a1;
30
31 TEXT(beginproblem());
32 BEGIN_TEXT
33 Consider the function
34 $f(x) = x^3 - quad x^2 + lin x + c$
35 By drawing a suitable picture, find a relation between the definite
36 integrals $$\displaystyle \int_1 ^2 f(x)\,dx$$ and $$\displaystyle \int_{y1}^{y2}f^{-1}(x)\,dx$$.
37 Use this relation to find the second of these two integrals
38 $PAR 39 $$\displaystyle \int_{y1}^{y2}f^{-1}(x)\,dx$$ = \{ ans_rule(30)\} 40$PAR
41
42 END_TEXT
43
44 ANS(num_cmp(\$ans));
45
46 ENDDOCUMENT();


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