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| 1 : | jj | 62 | ## DESCRIPTION |
| 2 : | ## Calculus | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('calculus', 'integrals', 'Partial Fractions') | ||
| 6 : | ## Tagged by YL | ||
| 7 : | |||
| 8 : | ## DBsubject('Calculus') | ||
| 9 : | ## DBchapter('Techniques of Integration') | ||
| 10 : | jjholt | 497 | ## DBsection('Integration by Partial Fractions') |
| 11 : | jj | 62 | ## Date('') |
| 12 : | ## Author('') | ||
| 13 : | ## Institution('ASU') | ||
| 14 : | jjholt | 473 | ## TitleText1('Calculus: Early Transcendentals') |
| 15 : | ## EditionText1('5') | ||
| 16 : | jj | 62 | ## AuthorText1('Stewart') |
| 17 : | jjholt | 473 | ## Section1('7.4') |
| 18 : | jj | 62 | ## Problem1('') |
| 19 : | |||
| 20 : | jjholt | 481 | ## TitleText2('Calculus: Early Transcendentals') |
| 21 : | ## EditionText2('6') | ||
| 22 : | ## AuthorText2('Stewart') | ||
| 23 : | ## Section2('7.4') | ||
| 24 : | ## Problem2('') | ||
| 25 : | |||
| 26 : | jj | 62 | &DOCUMENT; |
| 27 : | loadMacros( | ||
| 28 : | "PG.pl", | ||
| 29 : | "PGbasicmacros.pl", | ||
| 30 : | "PGchoicemacros.pl", | ||
| 31 : | "PGanswermacros.pl", | ||
| 32 : | "PGauxiliaryFunctions.pl" | ||
| 33 : | ); | ||
| 34 : | |||
| 35 : | |||
| 36 : | gage | 268 | TEXT(beginproblem()); |
| 37 : | jj | 62 | |
| 38 : | $p=random(1,5,1); | ||
| 39 : | $u=random(1,6,1); | ||
| 40 : | $r=random(-4,-1,1); | ||
| 41 : | $a=random(-3,3,1); | ||
| 42 : | $l=2*$a; | ||
| 43 : | $q=$u+$p*$a; | ||
| 44 : | $b=random(1,5,1); | ||
| 45 : | $c=non_zero_random(-3,3,1); | ||
| 46 : | $d=$p+$r; | ||
| 47 : | $e=$q+($c*$p)+($l*$r); | ||
| 48 : | $k=$a*$a+$b*$b; | ||
| 49 : | $f=($r*$k)+($c*$q); | ||
| 50 : | $g=$l+$c; | ||
| 51 : | $h=$l*$c+$k; | ||
| 52 : | $j=$k*$c; | ||
| 53 : | $hp=$p/2; | ||
| 54 : | $v=$u/$b; | ||
| 55 : | $funct="$hp*ln(x*x+$l*x+$k)+$r*ln(abs(x+$c))+$v*arctan((x+$a)/$b)"; | ||
| 56 : | |||
| 57 : | $p1 = nicestring([$d,$e,$f]); | ||
| 58 : | $p2 = nicestring([1,$g,$h,$j]); | ||
| 59 : | TEXT(EV2(<<EOT)); | ||
| 60 : | |||
| 61 : | The answer to this question contains absolute values.$BR | ||
| 62 : | The absolute value of a quantity w should be written abs(w).$BR | ||
| 63 : | Evaluate the integral. | ||
| 64 : | $BR | ||
| 65 : | $BR \[ \int \frac{$p1}{$p2} dx \] | ||
| 66 : | $BR \{ans_rule(80) \} | ||
| 67 : | EOT | ||
| 68 : | $ans=$funct; | ||
| 69 : | gage | 268 | ANS(fun_cmp($ans, mode=>"antider")); |
| 70 : | jj | 62 | |
| 71 : | &ENDDOCUMENT |
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