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Sat Jul 24 17:11:33 2010 UTC (2 years, 9 months ago) by ted shifrin
File size: 1217 byte(s)
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    1 ## DESCRIPTION
2 ## Multivariable Calculus
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('calculus','triple 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",
24            );
25
26
27 $showPartialCorrectAnswers = 1; 28 29 Context("Numeric")->variables->are(x=>'Real',y=>'Real',z=>'Real'); 30 31$a = random(1,5);
32 $b = random(1,3); 33 34 35$f = Formula("$a y")->reduce; 36$g = Formula("$b**2-x^2")->reduce; 37 38 @fn = ("1","y","z"); 39 @choice = NchooseK($#fn,1);
40 $h = Formula("@fn[@choice[0]]")->reduce; 41 42 @ans=(Compute("8*$a*$b^5/15"),Compute("32*$a*$b^7/105"),Compute("16*$a^2*$b^7/105")); 43$ans=@ans[@choice[0]];
44
45 TEXT(beginproblem());
46
47
48 Context()->texStrings;
49 BEGIN_TEXT
50
51 Let $$\Omega\subset\mathbb R^3$$ be the region bounded below by the $$xy$$-plane, above by $$z=f$$, and on the sides by $$y=g$$. Evaluate the integral
52 $\int_\Omega h\,dV \ .$
53
54 $PAR 55 56 57$PAR
58 \{ans_rule(10)\}
59
60
61 END_TEXT
62
63 ANS(\$ans->cmp);
64
65
66 ENDDOCUMENT();