##DESCRIPTION ## Write a difference of two integrals as a single integral ##This is setIntegrals0Theory/nttheo1.pg slightly cleaned up and expanded ##by Zig Fiedorowicz, Jan. 2001 ##ENDDESCRIPTION ##KEYWORDS('integrals', 'theory') ## Shotwell cleaned ## lcao , PAID on 11-24-2003 ## DBsubject('Calculus') ## DBchapter('Integrals') ## DBsection('The Definite Integral') ## Date('6/3/2002') ## Author('') ## Institution('') ## TitleText1('Calculus Early Transcendentals') ## EditionText1('4') ## AuthorText1('Stewart') ## Section1('5.2') ## Problem1('46') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PGbasicmacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$a= random(-10, 10); $a1 = random(2, 10);$a2 = random(2, 10); $a3 = random(1, 10);$b1 = random(1,3,.5); $b =$a+$b1;$c = $b+$b1; $d =$c+$b1; BEGIN_TEXT Let $$\displaystyle \int_{a}^{d} f(x)\, dx =a1, \ \int_{a}^{b} f(x)\, dx=a2, \ \int_{c}^{d} f(x)\, dx =a3$$.$BR$BR Find $$\displaystyle \int_{b}^{c} f(x)\, dx=$$ \{ans_rule( 20)\}$BR $BR and $$\displaystyle \int_{c}^{b} a1 f(x)- a2 \, dx=$$ \{ans_rule( 20)\} END_TEXT$ans1="$a1-($a2)-($a3)";$ans2="-($a1*($ans1))+$a2*$b1"; ANS(num_cmp($ans1), num_cmp($ans2)); ##set $PG_environment{'textbook'} in webworkCourse.ph if (defined($textbook)) { if (\$textbook eq "EllisGulick5") { BEGIN_TEXT This is similar to Problems 9-12 in Section 5.3 of the text. END_TEXT } } ENDDOCUMENT(); # This should be the last executable line in the problem.