View of /trunk/NationalProblemLibrary/ASU-topics/setCalculus/stef/stef7_4p1.pg

    1 ## 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 ## DBsection('Integration by Partial Fractions')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('7.4')
   18 ## Problem1('')
   19 
   20 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('6')
   22 ## AuthorText2('Stewart')
   23 ## Section2('7.4')
   24 ## Problem2('')
   25 
   26 &DOCUMENT;
   27 loadMacros(
   28 "PG.pl",
   29 "PGbasicmacros.pl",
   30 "PGchoicemacros.pl",
   31 "PGanswermacros.pl",
   32 "PGauxiliaryFunctions.pl"
   33 );
   34 
   35 
   36 TEXT(beginproblem());
   37 
   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 ANS(fun_cmp($ans, mode=>"antider"));
   70 
   71 &ENDDOCUMENT