LimitsOfIntegration1

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Answer Blanks in the Limits of Integration

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This PG code shows how to put answer blanks into the limits of integration.


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PG problem file Explanation

Problem tagging data

Problem tagging:

DOCUMENT();

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGunion.pl",
"answerHints.pl",
);

TEXT(beginproblem());

Initialization: We must use PGunion.pl for table formatting commands we will use to put the answer blanks in the limits of integration. We use answerHints.pl to help guide students toward the correct answer.

Context("Numeric");
Context()->variables->are(
x=>"Real", dx=>"Real",
t=>"Real", dt=>"Real"
);

$fpx = Formula("sin(x)"); 
$fpt = Formula("sin(t)");   

#
#  Display the answer blanks properly in different modes
#
Context()->texStrings;
if ($displayMode eq 'TeX') {
   $integral =
   '\(\displaystyle f(x) = '.
   ans_rule(4). 
   '+ \int_{t = '. 
   ans_rule(4). 
   '}^{t = '. 
   ans_rule(4).
   '}'. 
   ans_rule(20).
   '\)';
  } else {
   $integral =
   BeginTable(center=>0).
     Row([
       '\(f(x)=\)'.$SPACE.ans_rule(4).$SPACE.'\(+\displaystyle\int\)',
       '\( t = \)'.ans_rule(4).$BR.$BR.'\( t = \)'.ans_rule(4),
       ans_rule(20)],separation=>2).
   EndTable();
}
Context()->normalStrings;

Setup: The block of code that puts the answer blanks into the exponents correctly in HTML and TeX modes probably does not need to be modified.

Context()->texStrings;
BEGIN_TEXT
Find a formula for the function \(f(x)\) such that 
\( \displaystyle f'(x)= $fpx \) and \( f(2)=5 \).
$BR
$BR
$integral
END_TEXT
Context()->normalStrings;

Main Text: To display the integral with answer blanks in the limits of integration properly, we insert it using $integral.

$showPartialCorrectAnswers = 1;

ANS( Compute("5")->cmp() );
ANS( Compute("x")->cmp() );
ANS( Compute("2")->cmp() );
ANS( Compute("$fpt * dt")->cmp()
->withPostFilter(AnswerHints( 
  Formula("$fpx") => "Are you using the correct variable?",
  Formula("$fpx*dx") => "Are you using the correct variable?",
  Formula("$fpt") => "Don't forget the differential dt", 
))
);

Answer Evaluation: We use AnswerHints to guide the students to the correct answer.

Context()->texStrings;
BEGIN_SOLUTION
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;


COMMENT('MathObject version');

ENDDOCUMENT();

Solution:

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