Parent Directory
| 
Revision Log
Revision 1458 - (view) (download)
| 1 : | ted shifri | 1458 | ## DESCRIPTION |
| 2 : | ## Calculus | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('double integral') | ||
| 6 : | |||
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | ## DBchapter('Multiple Integration') | ||
| 10 : | ## DBsection('Iterated Integrals') | ||
| 11 : | ## Date('December 23, 2009') | ||
| 12 : | ## Author('Ted Shifrin') | ||
| 13 : | ## Institution('UGA') | ||
| 14 : | |||
| 15 : | |||
| 16 : | DOCUMENT(); | ||
| 17 : | loadMacros("PGstandard.pl", | ||
| 18 : | "PGunion.pl", | ||
| 19 : | "PGcourse.pl", | ||
| 20 : | "PGbasicmacros.pl", | ||
| 21 : | "PGchoicemacros.pl", | ||
| 22 : | "PGanswermacros.pl", | ||
| 23 : | "PGauxiliaryFunctions.pl", | ||
| 24 : | "Parser.pl", | ||
| 25 : | ); | ||
| 26 : | |||
| 27 : | TEXT(beginproblem()); | ||
| 28 : | |||
| 29 : | ## Do NOT show partial correct answers | ||
| 30 : | $showPartialCorrectAnswers = 0; | ||
| 31 : | |||
| 32 : | Context("Numeric")->variables->are(x=>'Real',y=>'Real'); | ||
| 33 : | |||
| 34 : | ## Do NOT show partial correct answers | ||
| 35 : | $showPartialCorrectAnswers = 0; | ||
| 36 : | TEXT(beginproblem()); | ||
| 37 : | |||
| 38 : | $a=random(2,5); | ||
| 39 : | $aa=$a**2; | ||
| 40 : | |||
| 41 : | |||
| 42 : | Context()->texStrings; | ||
| 43 : | BEGIN_TEXT | ||
| 44 : | |||
| 45 : | From a recent exam: | ||
| 46 : | $PAR | ||
| 47 : | Evaluate (without resorting to any untoward techniques of integration): | ||
| 48 : | |||
| 49 : | \[\int_0^{$a}\int_0^{$a} \frac{y^2}{\sqrt{x^2+$aa}} \,dx\,dy + | ||
| 50 : | \int_{$a}^{$a \sqrt 2}\int_{\sqrt{y^2-$aa}}^{$a} \frac{y^2}{\sqrt{x^2+$aa}} \,dx\,dy \ .\] | ||
| 51 : | |||
| 52 : | $PAR | ||
| 53 : | \{ans_rule(15)\} | ||
| 54 : | |||
| 55 : | END_TEXT | ||
| 56 : | |||
| 57 : | ANS(num_cmp(4/9*$a**3)); | ||
| 58 : | |||
| 59 : | ENDDOCUMENT(); |
| aubreyja at gmail dot com | ViewVC Help |
| Powered by ViewVC 1.0.9 |