Midterm 1 PExam Key

# Midterm 1 PExam Key - Math 1272 - 30 "PRACTICE"...

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Unformatted text preview: Math 1272 - 30 "PRACTICE" MIDTERM EXAM 1 6 February 2011 The real exam will contain seven (7) problems, one from each of the numbered categories. You may use scientific calculators and all necessary trig identities will be written on the board. \~ 1.) (Section 7.1) Integration by Parts a.) f~(sec2~)dt J l~+') - t ~lt Ai I S u:: * .J rA\!-= r> n >e.C 22 T (j.. t ~ J~ ~ J J- _ ~J _ . J :::. ~ fU!Y\'2*= 2. ~ _l ~~ 5:~ 7-f '"t _ ~ /11 -=:::::=========== I c + b.) f e-e (cosZ8)d8 :::::::= ( T - =. :: -e --- C,.ti _e> :: c.) f[ln (4X2)] dx 2.) (Section 7.2) Trigonometric Integrals 1-5/ a.) cos O~d ~ JCcosx)(l + sin x)dx 2 -= S ( I +!A.. ) JLi. LA. -=O-tl ~ j X Cory o..x l_ := U+ ~U'+- L ' _------ ' ? + 1 r",x "7 b.) sin odd f(sin 3 x)(cos 4 x)dx :: r foS''f~) ~~) U~y Jk" -; : 6 {-iFl(OJ '\0 (I- cor'),) U~}( tAx- -=u. r. fu. (1 -1.(1 'i vVA~ -==- L (- corLr) JIA ::= f(l/l-u )dl.( JC{ = == .. ~)( k - ~(/;- -)111-"* ( -= ~ ~SS-X J(sin 2 t)(cos't)dt -= ~ Lor"\ Ii c.) both even ~o f . - . (~ f(COl'f} = l ~ 21 cvr7..f =- ..LI.J-cClr2fl I c.J.- f-t{O f) Sf ~ ",,""21-,2. .,XI 0(:. J. Jf == ~ S"p,}"" 21- J~ .. 1~:W: :/-Xu ~ ~ ~'-nLf ~ t (l -UJf l.f-~) tA ~ ~1 f du. ~ 2~S 2.f . ~ ~ ~ - wf Lfi)Jr+k JL(~ ~ L' . (G l ( 1- _ 1 ~ iff)' +- ~(!\u.3 +- c (- ,__{_6_~;_~,--_ _- - - - - -: - - - -= I~ 1 - -h y.~ lif +- ~& ~ Y2-!j S""> d.) (rnx)(nx) J(sin3x) (sin6x)dx \ -.. r oJ ~~ Ft ul--- B~ 2: _ <.c J (A.-B - Cor(j B =~ r~S(-))<)-QJr{<h)]Jx- = ~~~~C~{-'r)J -k;.(q)')l +C Yl~ (- ,>c) ~ -- u!v oJ,J pw/ t I ~k f.) tan odd J(sec' x)(tan3 x )dx -: f( 1 U)<,CiOA'"-\ r.~ c. X~J fMI)r) cIx )~ -:: ~({QL -.des:.L~Y -(y\:ecy)(t.z.. x-J k ~ _ [.0. t ' r 2.. 'f. ::: s-e.-c'2 X - ( LA. C IA L_l)J~ :: fLu i_v.) Jq lj - ( --- ''- ---~ J "to 3.) (Section 7.3) Trigonometric Substitution a) va'-x" x a sinB ~ f ~dx _ ~ 5" " '" ~ (~) t-::- S-~& == _ , )"~ 5__1 1. _ + c.. j 4.) (Section 7.4) Rational FlU1ctions by Partial Fractions a.) linear factor(s) AY+--f ( fx x-l 2 +3x+2 dx ~ A-()C+L) +- B(Kff) ~ )( _( Pd-f. 2) ;; '3 (A--+ B) X = Lx' B -= {- It LA +- B ~ -( 2A 4- i-A -=- -! A::-.-2 -~ tt-L X~( aHy~-f2) b.) repeated linear factor(s) /3 c f:- f f (X+5)~(X-l) dx d.) repeated (irreducible) quadratic factor(s) - b- fovx lu/ - ~L~ } K~+tfl 5.) (Section 7.4) Rationalizing U-Substitution 1, 5I 32 a.) J'V2X-l d X 2x+3 _ - ~ r V\ (fAdu) - I(~:;) +-3 -: J-' lA2 L~Lf-'; ' t7.1A - - -.. - ~ 112- +tf ":;:::;. u::: J2x-7"" U+~-=-X "2 LA. '2.. ~ j 0- jt'f!JI{ ~ (A - ~ tan-I ( ~) +c J{,l ::: tty ~ ) -' LA lJ.: -= 5K w :::: LA "3 =-)( Jw ~ 3Lt'2J~ 2~JU. ~ J><. U~-KJ -:;;;f +w')- Jw -:::. > I 1- 2 -=~ ~_ I C(1)+C '" ~ ~-I( X c -l)J+ ~;{li;1I\ ~ / ,.1 vv + C --- ...
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## This note was uploaded on 02/02/2012 for the course MAP 2303 taught by Professor Bramson during the Fall '11 term at University of Florida.

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