** Using WeBWorK **

I have a Calculus 2 integration problem where I want students to be able to enter their answer using the arcsec (x) form of this inverse trig. function, so I have added this option to the problem as shown below.

But MathQuill does not treat it properly, but instead inserts 'operatorname{arcsec}' in place of "arcsec".

To eliminate this error, do I have to create a custom grader?  Or is there another way I could define the arcsec as a function that would work properly with MathQuill?

Thanks!

Paul

See image below for the error given and the problem code below that:

# DESCRIPTION
# WeBWorK problem written by Paul Seeburger, <pseeburger@monroecc.edu>
# ENDDESCRIPTION



## DBsubject(Calculus - single variable)
## DBchapter(Techniques of integration)
## DBsection(Trigonometric integrals)
## Date(2/5/2014)
## Institution(Monroe Community College)
## Author(Paul Seeburger)
## KEYWORDS('calculus', 'integral', 'antiderivatives', 'indefinite integrals', 'inverse trig', 'arcsec')

## Textbook tags
## HHChapter1('Integration')
## HHSection1('Inverse Trigonometric Integrals')

DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGchoicemacros.pl",
"hhAdditionalMacros.pl",
"parserFormulaUpToConstant.pl",
);
 
Context("Numeric");

$a = random(2,9,1);
$asq = $a*$a;
$b = random(2,5,1);
$bsq = $b*$b;
$c = $a*2+1;
$bound = Compute(1.01*($a/$b));

Context()->variables->set(x=>{limits=>[$bound, 10]});

Context()->functions->set( asec => {TeX => '\text {arcsec}'}, );

Context()->flags->set(
  reduceConstants=>0, # no decimals
  reduceConstantFunctions=>1, # combine 4+5*2?
  formatStudentAnswer=>'parsed', # no decimals
);

$aoverb = reduced_frac($a, $b);
$bovera = reduced_frac($b, $a);

$func = Compute("$c/(x*sqrt($bsq x^2 - $asq))");
$antider = Compute("($c/$a) arcsec(|$b x|/$a)");
$afunc = FormulaUpToConstant($antider." + C");

#$afunc->{test_at} = [[1, -$bound], [1, -$bound*2], [1, -$bound*10]];
$afunc->{test_at} = [-$bound, -$bound*2, -$bound*10];


TEXT(beginproblem());
Context()->texStrings;
BEGIN_TEXT

Antidifferentiate. You may need to transform the integrand
first.
$PAR
\(\displaystyle \int\frac {$c}{x \sqrt{$bsq x^2 - $asq}}\, dx =\)
\{ ans_rule(60) \}

END_TEXT
Context()->normalStrings;

ANS($afunc->cmp() );

Context()->texStrings;
BEGIN_SOLUTION
$PAR SOLUTION $PAR

Recognizing that this is NOT a natural log form integral, since we would need a factor of \(x\) in the numerator (and not in the denominator) for that, we check to see if this may be an inverse trig form integral by rewriting the denominator of the integrand. $PAR
We see that \( a = $a \), \( u = $b x \), and \( du = $b \, dx \), $PAR
and we recognize that the integral is in the $BBOLD arcsecant $EBOLD form, 
\[ \int\frac {du}{u\sqrt{u^2 - a^2}} = \frac{1}{a}\text{arcsec}\left(\frac {|u|}{a}\right) + C.\]
Then we are able to evaluate the integral as follows:
\[
  \int\frac {$c}{x \sqrt{$bsq x^2 - $asq}}\, dx =
  $c \int\frac {$b}{$b x \sqrt{($b x)^2 - ($a)^2}}\, dx
\]
\[
  = \frac {$c}{$a} \text{arcsec}\left(\frac{|$b x|}{$a} \right) + C
  = \frac {$c}{$a} \text{arcsec}\left($bovera |x| \right) + C.
\]

END_SOLUTION
Context()->normalStrings;


COMMENT('MathObject version');
ENDDOCUMENT();