View of /trunk/NationalProblemLibrary/Rochester/instructiveProblems/OldProblems/invtrigs7.pg

    1 ##DESCRIPTION
    2 ##KEYWORDS('integrals', 'trigonometric','substitution')
    3 ##ENDDESCRIPTION
    4 
    5 DOCUMENT();        # This should be the first executable line in the problem.
    6 
    7 loadMacros(
    8 "PGcourse.pl",
    9 "PG.pl",
   10 "PGbasicmacros.pl",
   11 "PGchoicemacros.pl",
   12 "PGanswermacros.pl",
   13 "PGauxiliaryFunctions.pl"
   14 );
   15 
   16 TEXT(beginproblem());
   17 $showPartialCorrectAnswers = 1;
   18 
   19 ###################
   20 #
   21 #  Setup
   22 
   23 $a = random(1,10,1);
   24 $b = random(1,6,1);
   25 $c1 = random(2,6,1);
   26 $c = $b+$c1;
   27 $d = random(2,100,1);
   28 $a1 = $c*$c-$b*$b;
   29 $a2 = $a*$a;
   30 $ab2 = 2*$a*$b;
   31 $rend = $c1/$a;
   32 $lend = 0;
   33 $funct = " $d*arcsin(($a*x+ $b)/$c)/$a ";
   34 
   35 $ans = $funct;
   36 ###################
   37 #
   38 #  Text
   39 
   40 TEXT(EV2(<<EOT));
   41 
   42 Evaluate the indefinite integral.
   43 $BR \[ \int \frac{$d}{\sqrt{$a1 -$ab2 x -$a2 x^2}} dx \]
   44 $BR \{ans_rule( 30) \}
   45 
   46 EOT
   47 
   48 ###################
   49 #
   50 #  Answers
   51 
   52 ANS fun_cmp("$ans + c",var=>'x',params=>['c'], domain=>[$lend,$rend] );
   53 
   54 ENDDOCUMENT();        # This should be the last executable line in the problem.