## DESCRIPTION ## Calculus ## ENDDESCRIPTION ## KEYWORDS('calculus','integration','fundamental theorem of calculus') ## Tagged by cmd6a 8/9/06 ## DBsubject('Calculus') ## DBchapter('Integrals') ## DBsection('The Fundamental Theorem of Calculus') ## Date('8/23/07') ## Author('K. Lesh') ## Institution('Union College') ## TitleText1('Calculus') ## EditionText1('7') ## AuthorText1('Anton') ## Section1('6.6') ## Problem1('4') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PGstandard.pl", "PGunion.pl", # Union College utilities "MathObjects.pl", "PGcourse.pl", # Customization file for the course ); TEXT(beginproblem()); ################################### # Setup $lower =-1; # left endpoint of the interval of integration$upper = 1; # right endpoint of the interval of integration $c = non_zero_random(2,5,1);$integrand = Formula("{$c} / {x^2+1}")->reduce; ################################### # Main text Context()->texStrings; BEGIN_TEXT Use the Fundamental Theorem of Calculus to evaluate the definite integral.$PAR $$\displaystyle\int_{lower}^{\,upper} integrand \,dx$$ = \{ans_rule(50)\} END_TEXT Context()->normalStrings; ################################### # Answers $showPartialCorrectAnswers = 1;$antideriv=Formula("$c tan^(-1)(x)");$ftc=$antideriv->eval(x=>$upper) - $antideriv->eval(x=>$lower); ANS(Compute("$c/2 *pi")->cmp); ## Using this to display pi in answer rather than usual ANS below #ANS(Real($ftc)->cmp); ################################### COMMENT('MathObject version'); ENDDOCUMENT();