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# Annotation of /trunk/NationalProblemLibrary/UCSB/Stewart5_5_3/Stewart5_5_3_16.pg

 1 : apizer 1647 ## DBsubject('Calculus') 2 : ## DBchapter('Integrals') 3 : ## DBsection('The Fundamental Theorem of Calculus') 4 : ## KEYWORDS('antiderivatives') 5 : ## TitleText1('Calculus') 6 : ## EditionText1('5e') 7 : ## AuthorText1('Stewart') 8 : ## Section1('5.3') 9 : ## Problem1('16') 10 : ## Author('') 11 : ## Institution('UCSB') 12 : 13 : DOCUMENT(); 14 : 15 : loadMacros( 16 : "PG.pl", 17 : "PGbasicmacros.pl", 18 : "PGchoicemacros.pl", 19 : "PGanswermacros.pl", 20 : "PGauxiliaryFunctions.pl" 21 : ); 22 : 23 : TEXT(&beginproblem); 24 : $showPartialCorrectAnswers = 1; 25 :$a=random(1,10,1); 26 : $b=random(1,10,1)*random(-1,1,2); 27 :$c=random(1,10,1)*random(-1,1,2); 28 : 29 : BEGIN_TEXT 30 : 31 : $PAR 32 : Let $$\displaystyle y=\int_1^{\cos(x)}{(b t + a \sin(t))}\,dt.$$ Use the Fundamental Theorem of Calculus to find $$y'.$$ 33 : 34 :$PAR 35 : $$y' =$$ \{ans_rule(50)\} 36 : 37 : END_TEXT 38 : 39 : ANS(fun_cmp("($b*cos(x)+$a*sin(cos(x)))*(-1)*(sin(x))", var=>["x","t"])); 40 : 41 : ENDDOCUMENT();