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# Annotation of /trunk/NationalProblemLibrary/OSU/accelerated_calculus_and_analytic_geometry_i/hmwk8/prob5.pg

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 1 : jjholt 314 ## DESCRIPTION 2 : ## Integration by Parts 3 : ## ENDDESCRIPTION 4 : 5 : ## KEYWORDS('Integration', 'Parts') 6 : ## Tagged by nhamblet 7 : 8 : ## DBsubject('Calculus') 9 : ## DBchapter('Techniques of Integration') 10 : ## DBsection('Integration by Parts') 11 : ## Date('') 12 : ## Author('') 13 : ## Institution('OSU') 14 : ## TitleText1('') 15 : ## EditionText1('') 16 : ## AuthorText1('') 17 : ## Section1('') 18 : ## Problem1('') 19 : 20 : jj 213 DOCUMENT(); 21 : 22 : loadMacros( 23 : "PG.pl", 24 : "PGbasicmacros.pl", 25 : "PGchoicemacros.pl", 26 : "PGanswermacros.pl", 27 : "PGauxiliaryFunctions.pl" 28 : ); 29 : 30 : $showPartialCorrectAnswers = 1; 31 : 32 : 33 :$a = random(1,7,1); 34 : $e = exp(1); 35 :$ans = "-$a *$e^(-$a) -$e^(-$a) + 1"; 36 : 37 : gage 269 TEXT(beginproblem()); 38 : jj 213 BEGIN_TEXT 39 : 40 : Use integration by parts to evaluate the definite integral. 41 :$BR $\int_{0}^{a} t e^{-t} dt$ 42 : $BR$BR \{ans_rule( 60) \} 43 : $PAR 44 : 45 : This is similar to problem 29 in section 7.1 of the text. 46 : END_TEXT 47 : 48 : gage 269 ANS(num_cmp($ans)); 49 : jj 213 50 : ENDDOCUMENT();

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