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| 1 : | gage | 5 | ##DESCRIPTION |
| 2 : | ## Integrals - Fundamental theorem of calculus | ||
| 3 : | ##ENDDESCRIPTION | ||
| 4 : | ##KEYWORDS('integrals', 'fundamental theorem of calculus') | ||
| 5 : | |||
| 6 : | ## Shotwell cleaned | ||
| 7 : | ## lcao , PAID on 11-24-2003 | ||
| 8 : | |||
| 9 : | ## DBsubject('Calculus') | ||
| 10 : | ## DBchapter('Integrals') | ||
| 11 : | ## DBsection('The Fundamental Theorem of Calculus') | ||
| 12 : | ## Date('6/3/2002') | ||
| 13 : | ## Author('') | ||
| 14 : | ## Institution('') | ||
| 15 : | jjholt | 453 | ## TitleText1('Calculus: Early Transcendentals') |
| 16 : | jjholt | 479 | ## EditionText1('6') |
| 17 : | gage | 5 | ## AuthorText1('Stewart') |
| 18 : | ## Section1('5.3') | ||
| 19 : | ## Problem1('3') | ||
| 20 : | |||
| 21 : | DOCUMENT(); # This should be the first executable line in the problem. | ||
| 22 : | |||
| 23 : | loadMacros("PGbasicmacros.pl", | ||
| 24 : | "PGanswermacros.pl", | ||
| 25 : | "PGauxiliaryFunctions.pl"); | ||
| 26 : | |||
| 27 : | TEXT(beginproblem()); | ||
| 28 : | $showPartialCorrectAnswers = 1; | ||
| 29 : | |||
| 30 : | $x1=random(2,6,1); | ||
| 31 : | $a1 = random(-1,1,2); | ||
| 32 : | $x2= $a1*$x1; | ||
| 33 : | $b1 = random(3,8,1); | ||
| 34 : | $c1 = random(-1,5,1); | ||
| 35 : | |||
| 36 : | BEGIN_TEXT | ||
| 37 : | Let \( \displaystyle f(x) = \int_{$c1}^x t^$b1 dt \). Evaluate the following. | ||
| 38 : | $BR | ||
| 39 : | $BR | ||
| 40 : | \( f'(x) = \) $SPACE \{ans_rule(20)\} $BR | ||
| 41 : | \( f'($x2) = \) \{ans_rule(20)\} | ||
| 42 : | END_TEXT | ||
| 43 : | |||
| 44 : | $ans1="x^$b1"; | ||
| 45 : | $ans2="$x2^$b1"; | ||
| 46 : | |||
| 47 : | ANS(fun_cmp($ans1)); | ||
| 48 : | ANS(num_cmp($ans2)); | ||
| 49 : | |||
| 50 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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