[npl] / branches / UGA / 7.2.8.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /branches/UGA/7.2.8.pg

Sat Jul 24 17:11:33 2010 UTC (2 years, 10 months ago) by ted shifrin
File size: 2387 byte(s)
Log message

    1 ## DESCRIPTION
2 ## Multivariable Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('calculus','iterated integral')
6
7
8 ## DBsubject('Calculus')
9 ## DBchapter('Multiple Integrals')
10 ## DBsection('Triple Integrals')
11 ## Date('December 23, 2009')
12 ## Author('Ted Shifrin')
13 ## Institution('UGA')
14 ## TitleText1()
15
16
17 DOCUMENT();
19            "PGbasicmacros.pl",
20            "PGchoicemacros.pl",
22            "PGauxiliaryFunctions.pl",
23            "Parser.pl",
25
26
28 $showPartialCorrectAnswers = 1; 29 30 Context("Numeric")->variables->are(x=>'Real',y=>'Real',z=>'Real'); 31 32$a = random(1,4);
33 $b = random(1,4); 34$c = random(1,4);
35
36 $f1 = nicestring([$a,-1],["","x"]);
37 $f2 = nicestring([$b,$c],["x","y"]); 38 39 40 41$C = Formula("0");
42 $D = Formula("$b x");
43 $E = Formula("0"); 44$F = Formula("$a-x"); 45 46$DD = Formula("$b x+$c*($a-x)"); 47$EE = Formula("(z-$b x)/$c");
48
49
50 TEXT(beginproblem());
51
52 BEGIN_TEXT
53 $BR 54 Assume $$f$$ is continuous. Interpret the following iterated integral as a triple integral $$\int_{\Omega} f\,dV$$ for the appropriate region $$\Omega$$ and then change the order of integration as directed. If you do not need 55 the second set of iterated integrals, fill in the first two limits as $$0$$; if you do need both, use the first set of iterated integrals for the lower of the two regions. 56 57$PAR
58
59 $\int_0^{a} \int_0^{f1}\int_0^{f2} f\left(\begin{array}{c}x\\y\\z\end{array}\right)\,dz\, dy\, dx\ = \int_a^b\int_C^D\int_E^F f\left(\begin{array}{c}x\\y\\z\end{array}\right)\,dy\, dz\, dx +$
60 $\int_{a'}^{b'}\int_{C'}^{D'}\int_{E'}^{F'} f\left(\begin{array}{c}x\\y\\z\end{array}\right)\,dy\, dz\, dx\ ,$
61 $BR 62 where 63$BR
64 $$a =$$ \{ans_rule(5)\}, $$b =$$ \{ans_rule(5)\},
65 $BR 66 $$C =$$ \{ans_rule(10)\}, $$D =$$ \{ans_rule(10)\}, 67$BR
68 $$E =$$ \{ans_rule(10)\}, and $$F =$$ \{ans_rule(10)\};
69 $PAR 70 and 71$BR
72 $$a' =$$ \{ans_rule(5)\}, $$b' =$$ \{ans_rule(5)\},
73 $BR 74 $$C' =$$ \{ans_rule(10)\}, $$D' =$$ \{ans_rule(10)\}, 75$BR
76 $$E' =$$ \{ans_rule(10)\}, and $$F' =$$ \{ans_rule(10)\};
77
78 END_TEXT
79
80 WEIGHTED_ANS(num_cmp(0),.05,num_cmp($a),.05); 81 WEIGHTED_ANS($C->cmp,.1); WEIGHTED_ANS($D->cmp,.1); 82 WEIGHTED_ANS($E->cmp,.1); WEIGHTED_ANS($F->cmp,.1); 83 84 WEIGHTED_ANS(num_cmp(0),.05,num_cmp($a),.05);
85 WEIGHTED_ANS($D->cmp,.1); WEIGHTED_ANS($DD->cmp,.1);
86 WEIGHTED_ANS($EE->cmp,.1); WEIGHTED_ANS($F->cmp,.1);
87
88
89 ENDDOCUMENT();