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| 1 : | jjholt | 197 | ## DESCRIPTION |
| 2 : | ## Calculus | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | jj | 144 | |
| 5 : | jjholt | 197 | ## KEYWORDS('integral' 'distance' 'length') |
| 6 : | ## Tagged by tda2d | ||
| 7 : | jj | 144 | |
| 8 : | jjholt | 197 | ## DBsubject('Calculus') |
| 9 : | ## DBchapter('Further Applications of Integration') | ||
| 10 : | ## DBsection('Arc Length') | ||
| 11 : | ## Date('') | ||
| 12 : | ## Author('') | ||
| 13 : | ## Institution('Rochester') | ||
| 14 : | ## TitleText1('') | ||
| 15 : | ## EditionText1('') | ||
| 16 : | ## AuthorText1('') | ||
| 17 : | ## Section1('') | ||
| 18 : | ## Problem1('') | ||
| 19 : | |||
| 20 : | jj | 144 | DOCUMENT(); |
| 21 : | loadMacros( | ||
| 22 : | "PG.pl", | ||
| 23 : | "PGbasicmacros.pl", | ||
| 24 : | "PGchoicemacros.pl", | ||
| 25 : | "PGanswermacros.pl", | ||
| 26 : | "PGauxiliaryFunctions.pl" | ||
| 27 : | ); | ||
| 28 : | |||
| 29 : | TEXT(beginproblem()); | ||
| 30 : | $as = 0; | ||
| 31 : | #$bs =0; | ||
| 32 : | #$as = non_zero_random(-1,1,1); | ||
| 33 : | $bs = non_zero_random(-3,3,1); | ||
| 34 : | $ac = non_zero_random(-2,2,1); | ||
| 35 : | $bc = non_zero_random(-2,2,1); | ||
| 36 : | $A = 2*$as*$ac; | ||
| 37 : | $B = (3*$ac*$bs) + (3*$as*$bc); | ||
| 38 : | $C = 6*$bs*$bc; | ||
| 39 : | $D = $as*$as - $ac*$ac; | ||
| 40 : | $E = 3*($as*$bs - $ac*$bc); | ||
| 41 : | $F = 3*$bs*$bs - 3*$bc*$bc; | ||
| 42 : | $G = $as*$as + $ac*$ac; | ||
| 43 : | $H = 3*$as*$bs + 3*$ac*$bc; | ||
| 44 : | $I = 3*$bs*$bs + 3*$bc*$bc; | ||
| 45 : | $J = $G + $H + $I; | ||
| 46 : | TEXT(EV2(<<EOT)); | ||
| 47 : | Find the length of parametrized curve given by $BR | ||
| 48 : | |||
| 49 : | \(x(t) = $A t^3 + $B t^2 + $C t, y(t) = $D t^3 + $E t^2 + $F t, \)$BR | ||
| 50 : | where t goes from zero to one. | ||
| 51 : | $BR | ||
| 52 : | Hint: The speed is a quadratic polynomial with integer coefficients. | ||
| 53 : | \{ans_rule(65)\} | ||
| 54 : | |||
| 55 : | EOT | ||
| 56 : | |||
| 57 : | $answer = $G + $H + $I ; | ||
| 58 : | ANS(num_cmp($answer)); | ||
| 59 : | |||
| 60 : | |||
| 61 : | &ENDDOCUMENT; | ||
| 62 : |
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