Merge pull request #1276 from dlglin/fixUnionIBPProb

Update Union IBP problem to PGML, and improve randomization

Author: pstaabp

OpenProblemLibrary/Union/setIntByParts/sc5_6_01.pg

@@ -16,48 +16,38 @@
 ## MO(1)
 ## KEYWORDS('calculus','integration','integration by parts')
 
-DOCUMENT();        # This should be the first executable line in the problem.
+DOCUMENT();    # This should be the first executable line in the problem.
 
-loadMacros(
-  "PGstandard.pl",
-  "PGunion.pl",
-  "MathObjects.pl",
-  "PGcourse.pl"
-);
+loadMacros('PGstandard.pl', 'PGML.pl', 'PGcourse.pl');
 
-TEXT(beginproblem());
-
-###################################
 # Setup
 
-$a = random(2,4,1);
-
-$integrand=Formula(" x e^{$a x} ");
+$a         = random(2, 9, 1);
+$integrand = Formula(" x e^{$a x} ");
 
-###################################
-# Main text
+Context()->flags->set(reduceConstants => 0);
+$antideriv = Formula("1/$a (x e^(${a}x) - 1/$a e^(${a}x))");
 
-Context()->texStrings;
-BEGIN_TEXT
+BEGIN_PGML
 Evaluate the indefinite integral.
-$PAR
-\( \displaystyle\int $integrand \, dx \)
-             = \{ans_rule(50)\} \( + C\).
-END_TEXT
-Context()->normalStrings;
 
-###################################
-# Answers
+[``\int [$integrand] \, dx ``]=
+[_]{$antideriv->cmp(upToConstant=>1)}{50} [` + C`].
+END_PGML
 
-$showPartialCorrectAnswers = 1;
-Context()->flags->set(reduceConstants=>0);
+BEGIN_PGML_SOLUTION
+Calculate the integral using integration by parts.
 
-$antideriv = Formula( "1/$a (x e^(${a}x) - 1/$a e^(${a}x))");
+Let [`u=x`] and [`dv=e^{[$a]x}dx`]
 
-ANS($antideriv->cmp(upToConstant=>1));
+Then [`du=dx`] and [`v=\frac{1}{[$a]}e^{[$a]x}`].
 
-###################################
+[``\int u\,dv=uv-\int v\,du``], so
 
+[``\begin{eqnarray}\int xe^{[$a]x}\,dx & = & x\left(\frac{1}{[$a]}e^{[$a]x}\right)-\int \frac{1}{[$a]}e^{[$a]x}\,dx\\
+& = & \frac{1}{[$a]}\left(xe^{[$a]x}-\int e^[$a]x\,dx\right)+C\\
+& = & \frac{1}{[$a]}\left(xe^{[$a]x}-\frac{1}{[$a]} e^[$a]x\,dx\right)+C
+\end{eqnarray}``]
+END_PGML_SOLUTION
 
-;
 ENDDOCUMENT();