Test2_key_F05 - 5 M I MthSc 108 Fall 2005 T2 V1 8.1 — 8.5...

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Unformatted text preview: 5 M I MthSc 108 - Fall 2005 T2 - V1 8.1 — 8.5, 8.8 Evaluate the following integrals. Be sure to show all work. In particular, write out substitutions and choices for parts. 1. Isin3 xcos2 x dx (11 pts) : Smx (I‘GOSZX)C,O$szX La: QaSK duo: 'ngJ K : (bf v.3 +C GWMDLJmmstJ 5 '3— (Z- ldwimz) MwW : Cos‘fx _ c053x + C WWW éEfiidM.’ DIU’NLL. O'ALWW *W W W J . W- WW W W7E‘ZFW 2. 1J'x4"dx LL: dv: ‘1‘xe (11915) 0 M=dX V: i: /n'-/ : K'4LI _ £C/ In’+ o fn‘l“ X. . . = 4 — L)’ WM) I” (but); 0 31:; W =— 4 - L —/—- #d‘t Way In“! (Irv-t)” (M4) = i. 3 IfiLl Int}?— Points on nae = 22 MthSc 108 — Fall 2005 T2 — V1 8.1 - 8.5, 8.8 1 3. d IV16+X2 X yrs/me (11pts) 3;. = game My " =fA/sw29cle on: etaufede "‘ 49496 glue: W =jmede =fl4~fme+mel+c WJHOVJF‘ 6Wwf =<L~Wy- 4 3—: w ”535 MW 4. [(x2+2)sin(2x)dx (L: 172,. ,;1 ‘ JV: gm 2X 4 X (11pts) U» ~ZK 01w: 74¢ (1* VZ'Zé: 6030,21 fini- 141 : (til) ““37" 9!}:ch 2. ’1' : —' +7- @521 + Etc/052x41 : >< .dvzcwszxclx 7- dkfiJK \l: 6m2x ,L 7. c: —- +7— coszx + xsmlx - 58ml! c196 7’ 1 T Points on nae = 22 MthSc 108 -— Fall 2005 T2 - V1 8.1 — 8.5, 8.8 5 313233;)“ u- Cos 59 (11 pts) 0 dL=—3$m56de A I d K=0~=7 w=w50=$ : .—————— ' .5: a” " .z : $052: :1" ‘ 5 x 7% a LL 6 7K -3 k W— ‘5 '5 1 QWMWJ’SW :5 I3 V? = "L7— ,_ .__l—— f‘ _!_ : l 6M . W?) ‘1 ‘7 ‘1 6i 6. Eligdx u: flan—x AV: [LC/K ‘ (12pts) 2 Mt-Ldk V3 >4" = ‘2’!" X ”I K I: ;-_- M $132: CL 5( A ' ~ 3 {rfim a, K" W ,. 1: b — . .2: W ~wi'M +51%] W W“ — 5L '1’ ¢ ea“ ’56“; wt W515? 1; —/ “0"; W43" MAE” _M ‘wat avx'l— )(H ] W d 13”” . - ‘ ————— + + 1'“ . ' ‘ 52W 10 1. I " WW ”0 W I; t (2':ng 4’ 7» b g“ «R 1 Points on ”as = 23 MthSc 108 — Fall 2005 T2 - V1 " 8.1 — 8.5, 8.8 3x2—10x+1 1- —--~~— ,_ 4 im .,._ 77"”st (I +I)(x'5) Kalil X'5 5,: t (h, {a [0-1—4— 3xblox+ I :(nuB 1’5 + 0431‘) «new. 1 I . MW‘W 5&7; — AL—SAX+gX-—EE+CI}7—+C fiwéwlfi W‘ K: " ‘ ‘ 5A+B : —-— IO 5—); "6E: 94.0:1L. "' ‘I'C = V ea: "55-14: I '55=o «>75 =0 “‘5 9:2. 5x7’10x+\ 4 2‘ + J— clx ’ Points on oae=12 MthSc 108 — Fall 2005 T2 — V1 8.1 — 8.5, 8.8 8. a. "T Write out the form of the partial fraction decomposition of the function W __. ' W. 3x4+2x3—6x2+x—1 V- éWJ W » M w: ’54— 453‘ DO NOT DETERMINE THE NUMERICAL VALUE 8 OF THE COEFFICIENTS. (9 pts) ”QM/$1” X X? K?+Ll x" (X—O$ The ellipse x2 +9y2 =1 is depicted below. The shaded region is divided into two parts: AI (above the x-axis) and A2 (below the x-axis.) Find an equation for the portion of the ellipse graphed on or above the x-axis. (2 pts) ' x3+4%1=l q 31 = I « 1 T 7' g i , y. T ’4'“ 47:77 . Points on page = 11 I 6 MthSc 108 — Fall 2005 T2 — V1 I b. 0. Find an expression for the area of the shaded region labeled A1. AMWP6H,= [Al/34x} d/X Wkflfiww 8.1 — 8.5, 8.8 (4 pts) _. L AWMW / WWW ’12 Find the area of the entire shaded region. ‘ (6 pts) I J’ A -‘ { “ ' " ’0 cl A X 2— " .._.———-e—- )5 . y? 3 4/ (-40— L =‘ 305 (9 d6 ‘V/u; 5 (A,- ‘ = ,1, 5+ 6/0526 J a d a "“70 7%, 1 4’ :gir/ _Ai__3_],"nf £5: 5 b 3 '3 Z74- Pointson -a-e=10 Z MthSc 108 — Fall 2005 T2 — V2 8.1 — 8.5, 8.8 Evaluate the following integrals. Be sure to show all work. In particular, write out substitutions and choices for parts. 1. Icosa xsinzxdx ‘ (11pts) :jwsx(l/SW¢K)§m1xdx LL: Smx clu_= cosxclx -: {RILL” Dv+> A K] 3 5 ’ Ur " // u) +C 5 5 . ij Sagx 2” —— +0 3 5 2. :[x7xdx LL: X m17£ x (11pts) ° way v: 7* 7 ‘ A? _. K x I (73- p7 l0 ' imply = .11... __ 3‘ ’ M (Ma Points on -_ae = 22 MthSc 108 — Fall 2005 T2 — V2 1 3. dx I«125+x2 =j ism/294.9 5W8 ryfleede : Almaty/mafia V7v§+11 K + —— 5 5 fC =19. 4, flxz —2)cos (2x)dx u. : 17'- A Aw=011cly (1113:5923: —fx M021 dry 1. '5 <X________ 9‘):W°§t+ Kcoslx "fiZi-"d 8.1 — 8.5, 8.8 (11 pts) Au: coslkd K (“pts) :sz 7.. av: Sung—Kelsi V: - cos 2.x 7, ’ i=6): (1‘4 soggy _L,, ) + stcoszx ; Smlx+c :L a. 5L Points on gage = 22 I 3 MthSc 108 — Fall 2005 T2 — V2 8.1 — 8.5, 8.8 gcos(2¢9) a: W 525 , . l 5' gsin‘(29)d9 M : «96,05 :28 d9 (11pts) I 2’. if it} 42; 51-77%) LL M: ¢ 41/ (7’ 1" (.rr“ , 1/ — —L 5—1-5 I U 174’? “.véw 7; $ '5 A " f “K ! ’ -I ‘ I q (91* + - ’/ +/ , ’7 y” "’ ‘0 f?) 9 3 7 ml .. 6 J— JJJM M: J W doc = id} V: )(L , ”IL, -1 74” ' t = _Q,~x ....L—— “. gym; 'Mt ”Lit; + L; t ' 15—360 at; [y 2 "L 5 7:: : M [“I 9M5 I \t] 0‘ ,4? — f - ”L {a ”43;“ I? L” 6 Points on o-ae = 23 4 MthSc 108 — Fall 2005 T2 — V2 8.1 - 8.5, 8.8 3X2—6x+1 7' I(x2 +1)(x-3) dx (12 pts) gia'rlgx—ll : ”1+5 _1__ a Q“ ‘X 1'5) £1 + . H EMU—Lawn = <41+5><¥as>+c<192¥l> - AxtéAX-FEDSL’SEierly-i-C, IDCL=I0 (Ls! W AC7, ”615M: I «35:0 5:0 Points on nae =12 MthSc 108 — Fall 2005 T2 — V2 8.1 — 8.5, 8.8 8. Write out the form of the partial fraction decomposition of the function 3X‘—5x3+2x2+x—11 x2 (x2 +9)(x2 +2x+1) DO NOT DETERMINE THE NUMERICAL VALUE S OF THE COEFFICIENTS. (9 pts) :H+§+OM+D+DTE K 51” 1 3‘ .,. q 51-: I (H 9” 9. The ellipse x2 + 4y2 =1 is depicted below. The shaded region is divided into two parts: A, (above the x-axis) and A2 (below the x-axis.) a. Find an equation for the portion of the ellipse graphed on or above the x-axis. (2 pts) 58:1“ ‘7L 3,1: l 17L 32‘ = I — 1 3, 81 t I a I“ L7; ? :. 4/7177: T l ~W_ _ _ __ Pointson a e=11 6 MthSc 108 — Fall 2005 T2 — V2 8.1 — 8.5, 8.8 b. Find an expression for the area of the shaded region labeled A1. (4 pts) I Coot,» etc/A, : fx/I-x‘k 9L5! A '1 c. Find the area of the entire shaded region. ‘ (6 pts) ' . K . ,L 4/ I—— 1 or i . . /’V /V I’K‘V “7 yd' Lrfl/WQ €75 9’ aosQwW—w' x=/Z~fiC—) {Ml(fi) w/y r zyl S Haasze 5L9 ‘ ‘ /z. TV/L ‘2 51: la ezméfi)’ . = g, 7' 4f- ”b -: l 1: , 1: 4. WW _. MH/3 /‘ L’ W H 7* z ; ti — 4:5: w L» g C. L ’E— "% 'R'ILLA, is 17(0_'\I§’: (7’ lb 3 Points on -a_e =10 ...
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