Sol-162E2-F09 - MA 162 EXAM 2 Test 01 Fall 2009 1 Which of...

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Unformatted text preview: MA 162 EXAM 2 Test 01 Fall 2009 1. Which of the following integrals arises when one makes a suitable trigonometric substitution to compute mdm M: Z/Jkéfipc 6) O /4sin2 0d9 =ZW6’96459 sin 20 (“if m” 2W6 13- flow do i;- [7"WLZQ Z Cfl‘éé) £6 C. / tan26se00d0 Zc’aaé 2 D. /:::ng6 j ell/£141; 6) £9 / sin2 (9 E. d0 400826 4 d3? 2. Compute /2 152—4. />¢:: Z.4¢&6 , A- 1nW§+2> 4&0 r; ZméQ fail/£49655 B. éln(2\/§+3) \/ Abzvé’": ZZ/LJu/Lé’ 1 C. \/§+§ln(\/§+1) :5 W 6467 @ 1n<2+¢§) \ljf 2— L}- Zia/2469 E. 2ln(2\/§+3) “:2: {$664469 :A/LLIW€6+Z/Z£4bQ/+C 4a W Z Z— ' fwd—55+ :4)+C 6L .2 'W—‘WW = m/AMEU ~AW<Z+ W?) MA 162 EXAM 2 Test 01 Fall 2009 22: + 5 3. Evaluate / m dill. A. 3ln|m2+2m+2|+tan‘1(m2+2:c+2)+C W HZ/WLZ £30 + 4&5 ‘ "7 MELZM #2, 05142407132. Inlar:2 +2m+2| +3tan_1(:c+ 1) +0 C. lnlm2+2x+2|+ ,V (Z 0PM) +/ D. ——-— C w2+2m+2+ 2$+2+3tan"1(:13+1) +0 .w/ _1 Z E. 2111|2cc+2|+3tan (:1:+1)+C '7; MZM+w+ 22+ 3 “fizz/M» (AN/NC 4. What is the form of the partial fraction decomposition of {3+2 (:3 — 1)2(x + 1)(a:2 +4)” A A + B +C$+D ' (ac—1P x+1 (502+4)2 A B C D E B. ___ w—1+(a:—1)2+$+1+x2+4+(x2+4)2 A B C’J:+D C. m—l+ac+l+ x2+4 D D. A +Bac+C m+E F$+G 33—1 5132—1 + x2+4 +(zv2+4)2 " A B C Dx—i—E Fw+G x—l+(x—1)2+x+1+ m2+4 +(:I:2+4)2 2 MA 162 EXAM 2 Test 01 Fall 2009 1 4 5. Evaluate /0 mdm' E A- 1n2+1n4—1n3 mi 2 fl + ‘ B 112 14 313 (AL+/)[/w+3) AMI Aw} . 5 n _ n +5 n ‘ 1 17” : flZ/WZ} '4' 5 [04+]) 0. §(ln2—ln4+3ln3) 5 0 2; Z R 2(ln2+21114—1113) 1L :5 :z :2 .5, ‘ fl " fl Z) 2(ln2—1n4+1n3) %/4 +5 - if f / :Wi—M :5 (442.: 6&0 Aba+4f401~3 a ~/§¢+’3 :: Z L/bLZ/VJ‘H/ _. Z L/VLZ/S:‘7”3/:] 31’ Z (Ln/LZ Vim/17L 7444;?) MA 162 EXAM 2 Test 01 Fall 2009 1 d3: 6. Evaluate 0 fi+ 1. Z {421/770 44*: a, A. 1+1n2 £31): 2305540 B. 2—4ln2 ”A :‘ I Z 4,4621», :: .5 4' A C. —21—+21n2 I Milk] Z0“ flH-l 2—21n2 a, :2 / "h” / E. 2+}ln2 4+7 fli‘H 2 ~::: Z / W KL, 5554; t: Z (a e. M( féaL/O +6 56%] / :2 (w; 4741/; H» + c, 57%... mmmfl ‘9 .2: 2.725%; a 7. Find the length of the curve f (m) = 1n(sec m), 0 S x 3 7r/ 3. £5934) : / [flaw my» 2: @7444 A. ln(1+\/§) .m&% B. \/§+\/§ 7&9: WX4L A: W éép G. 1n(¢§+¢§) 7 D. 1+\/§ : flfl’f/yl @ ln(2+\/§) 0/3 F 4 E‘ [M40 fizz/1‘" : 4/24 //¢4€:/>O +i7u/qo/j /5 a /0 :- L/A ( Z + V?) MA 162 EXAM 2 Test 01 Fall 2009 8. A surface is generated by rotating the curve 31 = 2\/1 + :13, 0 S on S 2, about the x—axis. Find the surface area of the surface. 2 A £2: - I A. §3 2—f S : 3 2,17% 4% Ab W735 3( 2) 0 B. %75(\/§—\/§) Z 3 S 2, nz7TZWl/Efi 4% D. Z(«E—1) Vii—AA & Z1 , a: z E 3“”) :: LHT Elk—+3140 -*= flflzm) J , 3/ d5 3 c3 2: 5%?(9—2 Z) 9. A lamina of uniform density has the shape of the region bounded by yzw, and y2m4. 3 The area of the region is 1-6 Which expression gives the y—coordinate g of the center of mass. ’,. Z “2,. A _ 10 1(2 5)d . = — a: — M: (M)‘(/>j)é@a y 30 06:” A0 Z. 5 1 B. y: 3/0 (x—m4)2dm “$326350in Wm 1 C. y: —0—7T/01(x2—:B5)da: E]: 5/2 2 /0 J-[QV engaéjc . y: :1)le ‘538 1071' 2 2%; (Ma/”926% E' “T o‘Hs)“ r a I 5'! ML &&0 :2 f 67th ‘njtééfi? . II and III converge. Idiverges. 1 “9/ M q__/ M B. I and II converge. III diverges. <3 I _._/_, (947/10 :2: L/// AM [C] : mag}, C. II converges. I and III diverge. ”0 (Cw-5G "" D. I, II and III converge. M I ” ”Lag/X) . 2 U/7 j/ , / E. I, II and III diverge. / ,2“ [’0 77px) 7 )2 ' I I . Manama/z 7L +J— 3.... 127‘ Mrczm g 12 my /7'" Z I???” 157 /7“ 77 Ag} Ad 6 0” Z I; V TH/z: Céflflfl/V/ficfl/V 72:; 77 firiéoé@o (ML/R6153, 'Z 3:5ZW—MW6Z76 0 (3 MA 162 EXAM 2 Test 01 Fall 2009 10. The curve y = 6‘”, 0 S a: g 2, is rotated about the y—axis. Which integral gives the surface area of the surface of revolution. 2/? A. /227rem 1+€2md$ 3—» ~Mr£<b 0 ‘ ’ 2 CD @/ 27mv1+62$dw 0 5&4»: /7’“L%%>Z%¢: MFA 0' Ammo” 2 D. 7rme2m V 1 + 62:13 d3: 2 E. / 71‘62m dm 0 11. Which statement is true about the following improper integrals. 1 oo oo - 2 I. / ldw II. / ids; III. / sm2$dm _1£IZ' 1 6w 77' ”4’2“ ...
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