## 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", ); TEXT(beginproblem()); install_problem_grader(~~&std_problem_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"); $vol = Compute("pi"); # # Display the answer blanks properly in different modes # Context()->texStrings; if ($displayMode eq 'TeX') { $integral = 'Volume = $$\displaystyle' . '\int_{'. ans_rule(4). '}^{'. ans_rule(4). '}'. ans_rule(30). ' = '. ans_rule(10). '$$'; } else {$integral = BeginTable(center=>0). Row([ 'Volume = $$\displaystyle\int$$', ans_rule(4).$BR.$BR. ans_rule(4), ans_rule(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 $integral END_TEXT Context()->normalStrings; ##################################### # Answer Evaluation ANS($upper->cmp() ); ANS( $lower->cmp() ); ANS($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?", )) ); ANS( $vol->cmp() ); ##################################### # Solution Context()->texStrings; BEGIN_SOLUTION${PAR}SOLUTION:\${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version. Gives full credit only if all answers are correct.'); ENDDOCUMENT();