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| 1 : | jj | 213 | DOCUMENT(); |
| 2 : | ##DESCRIPTION | ||
| 3 : | ##KEYWORDS('integrals', 'integration by parts') | ||
| 4 : | ##ENDDESCRIPTION | ||
| 5 : | |||
| 6 : | loadMacros( | ||
| 7 : | "PG.pl", | ||
| 8 : | "PGbasicmacros.pl", | ||
| 9 : | "PGchoicemacros.pl", | ||
| 10 : | "PGanswermacros.pl", | ||
| 11 : | "PGauxiliaryFunctions.pl" | ||
| 12 : | ); | ||
| 13 : | |||
| 14 : | $showPartialCorrectAnswers = 1; | ||
| 15 : | |||
| 16 : | |||
| 17 : | $a = random(1,7,1); | ||
| 18 : | $e = exp(1); | ||
| 19 : | $ans = "-$a * $e^(-$a) - $e^(-$a) + 1"; | ||
| 20 : | |||
| 21 : | gage | 269 | TEXT(beginproblem()); |
| 22 : | jj | 213 | BEGIN_TEXT |
| 23 : | |||
| 24 : | Use integration by parts to evaluate the definite integral. | ||
| 25 : | $BR \[ \int_{0}^{$a} t e^{-t} dt \] | ||
| 26 : | $BR $BR \{ans_rule( 60) \} | ||
| 27 : | $PAR | ||
| 28 : | |||
| 29 : | This is similar to problem 29 in section 7.1 of the text. | ||
| 30 : | END_TEXT | ||
| 31 : | |||
| 32 : | gage | 269 | ANS(num_cmp($ans)); |
| 33 : | jj | 213 | |
| 34 : | ENDDOCUMENT(); |
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