## DESCRIPTION ## Integral calculus: volume of solids of revolution ## ENDDESCRIPTION ## KEYWORDS('Integrals', 'volume of solids of revolution') ## DBsubject('WeBWorK') ## DBchapter('WeBWorK Tutorial') ## DBsection('Fort Lewis Tutorial 2011') ## Date('10/20/2010') ## Author('Paul Pearson') ## Institution('Fort Lewis College') ## TitleText1('') ## EditionText1('') ## AuthorText1('') ## Section1('') ## Problem1('') ############################### # Initialization DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "PGunion.pl", "answerHints.pl", "weightedGrader.pl", ); TEXT(beginproblem()); install_weighted_grader(); $showPartialCorrectAnswers = 1; ################################ # Setup Context("Numeric"); Context()->variables->are( x=>"Real", dx=>"Real", y=>"Real", dy=>"Real" );$f = Compute("x"); $g = Compute("x^2");$upper = Real("1"); $lower = Real("0"); # answers below are intentionally wrong$int = Compute("( pi x - pi x^2 ) dx"); $vol = Compute("pi"); @weights = (5,5,40,50); # # Display the answer blanks properly in different modes # Context()->texStrings; if ($displayMode eq 'TeX') { $integral = 'Volume = $$\displaystyle' . '\int_{'. NAMED_ANS_RULE("lowerlimit",4). '}^{'. NAMED_ANS_RULE("upperlimit",4). '}'. NAMED_ANS_RULE("integrand",30). ' = '. ans_rule(10). '$$'; } else {$integral = BeginTable(center=>0). Row([ 'Volume = $$\displaystyle\int$$', NAMED_ANS_RULE("upperlimit",4).$BR.$BR. NAMED_ANS_RULE("lowerlimit",4), NAMED_ANS_RULE("integrand",30).$SPACE.' = '.$SPACE. ans_rule(10), ],separation=>2). EndTable(); } Context()->normalStrings; ##################################### # Main text Context()->texStrings; BEGIN_TEXT Set up and evaluate an integral for the volume of the solid of revolution obtained by rotating the region bounded by $$y = f$$ and $$y = g$$ about the $$x$$-axis. $BR$BR $integral END_TEXT TEXT(MODES(TeX=>"",HTML=> "${PAR}${BITALIC}${BBOLD}Note:${EBOLD} You can earn$weights[0]${PERCENT} for the upper limit of integration,$weights[1]${PERCENT} for the lower limit of integration,$weights[2]${PERCENT} for the integrand, and$weights[3]${PERCENT} for the finding the volume. If you find the correct volume, you will get full credit no matter what your other answers are.${EITALIC}")); Context()->normalStrings; ##################################### # Answer Evaluation NAMED_WEIGHTED_ANS( "upperlimit" => $upper->cmp(),$weights[0] ); NAMED_WEIGHTED_ANS( "lowerlimit" => $lower->cmp(),$weights[1] ); NAMED_WEIGHTED_ANS( "integrand" => $int->cmp() ->withPostFilter(AnswerHints( Formula("pi x - pi x^2 dx") => "Don't forget to multiply every term in the integrand by dx", Formula("pi x - pi x^2") => "Don't forget the differential dx", Formula("(pi x^2 - pi x)*dx") => "Is the parabola above the line?", Formula("pi x^2 - pi x") => "Is the parabola above the line?", )),$weights[2] ); CREDIT_ANS( $vol->cmp(), ["upperlimit","lowerlimit","integrand"],$weights[3] ); ##################################### # Solution Context()->texStrings; BEGIN_SOLUTION ${PAR}SOLUTION:${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version. Weights each answer blank separately, and the last answer provides full credit for all other answer blanks.'); ENDDOCUMENT();