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| 1 : | jjholt | 321 | ## DESCRIPTION |
| 2 : | ## Calculus | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('calculus','integration','fundamental theorem of calculus') | ||
| 6 : | ## Tagged by cmd6a 8/9/06 | ||
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | ## DBchapter('Integrals') | ||
| 10 : | ## DBsection('The Fundamental Theorem of Calculus') | ||
| 11 : | dpvc | 882 | ## Date('8/23/07') |
| 12 : | jjholt | 321 | ## Author('K. Lesh') |
| 13 : | ## Institution('Union College') | ||
| 14 : | dpvc | 882 | ## TitleText1('Calculus') |
| 15 : | ## EditionText1('7') | ||
| 16 : | ## AuthorText1('Anton') | ||
| 17 : | ## Section1('6.6') | ||
| 18 : | ## Problem1('4') | ||
| 19 : | jjholt | 321 | |
| 20 : | jj | 248 | DOCUMENT(); # This should be the first executable line in the problem. |
| 21 : | dpvc | 882 | |
| 22 : | jj | 248 | loadMacros( |
| 23 : | dpvc | 882 | "PGstandard.pl", |
| 24 : | "PGunion.pl", # Union College utilities | ||
| 25 : | "MathObjects.pl", | ||
| 26 : | "PGcourse.pl", # Customization file for the course | ||
| 27 : | jj | 248 | ); |
| 28 : | |||
| 29 : | gage | 1299 | TEXT(beginproblem()); |
| 30 : | jj | 248 | |
| 31 : | dpvc | 882 | ################################### |
| 32 : | # Setup | ||
| 33 : | jj | 248 | |
| 34 : | dpvc | 882 | $lower =-1; # left endpoint of the interval of integration |
| 35 : | $upper = 1; # right endpoint of the interval of integration | ||
| 36 : | $c = non_zero_random(2,5,1); | ||
| 37 : | jj | 248 | |
| 38 : | dpvc | 882 | $integrand = Formula("{$c} / {x^2+1}")->reduce; |
| 39 : | jj | 248 | |
| 40 : | dpvc | 882 | ################################### |
| 41 : | # Main text | ||
| 42 : | jj | 248 | |
| 43 : | dpvc | 882 | Context()->texStrings; |
| 44 : | jj | 248 | BEGIN_TEXT |
| 45 : | dpvc | 882 | Use the Fundamental Theorem of Calculus to evaluate the definite integral. |
| 46 : | jj | 248 | $PAR |
| 47 : | dpvc | 882 | \( \displaystyle\int_{$lower}^{\,$upper} $integrand \,dx \) |
| 48 : | = \{ans_rule(50)\} | ||
| 49 : | jj | 248 | END_TEXT |
| 50 : | dpvc | 882 | Context()->normalStrings; |
| 51 : | jj | 248 | |
| 52 : | dpvc | 882 | ################################### |
| 53 : | # Answers | ||
| 54 : | |||
| 55 : | jj | 248 | $showPartialCorrectAnswers = 1; |
| 56 : | |||
| 57 : | dpvc | 882 | $antideriv=Formula("$c tan^(-1)(x)"); |
| 58 : | $ftc=$antideriv->eval(x=>$upper) - $antideriv->eval(x=>$lower); | ||
| 59 : | |||
| 60 : | ANS(Compute("$c/2 *pi")->cmp); ## Using this to display pi in answer rather than usual ANS below | ||
| 61 : | #ANS(Real($ftc)->cmp); | ||
| 62 : | |||
| 63 : | ################################### | ||
| 64 : | |||
| 65 : | gage | 1328 | |
| 66 : | COMMENT('MathObject version'); | ||
| 67 : | ENDDOCUMENT(); |
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