172sP EXAM 1 SOLUTIONS

# 172sP EXAM 1 SOLUTIONS - Math 172 ‘ EXAM 1 February 10,...

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Unformatted text preview: Math 172 ‘ EXAM 1 February 10, 2010 Name: “M ID#: m Section#: ______ SHOW APPROPRIATE WORK or EXPLANATION on each problem for full credit. Box or circle your ﬁnal answers. Calculators/ note sheets are NOT allowed. Numbers in the ] indicate What each problem is worth. Check‘the board for useful info. ' Formulae: sin(2m) = 2 sin(:I;) cos(m) sin2(x) = %[1 — cos(2x)] cos2(a:) = a1 + cos(2:v)] 1 —— sin2(x) :2 cos2(m) tan2(a:) + 1 2 sec2(x) secz(:1:) — 1 = tan2(m) 1. [10 each] Evaluate each of the following integrals: :10 + 8 —— d a) / :33 +23:2 x Pah‘x‘al 0950,70; X+g .ﬁ—H‘} 171’), : AXE Ewen) eC can) 2 : x (kn) X—l 1. X1 (X n) ,9 )(L 36 a Maw. ABA am x+£= Ava Bxbmh CW), [Emmi X= O a? g: 2c ’57 (:7 . 3 ‘ .2 2 Li A X4 0! a a “a , X : __/—\ ’W‘ + >( go ' fxlﬂx" jx—r; >4 X1) 3 E § E E 3 E E a b) /x3v4—x2 d1: /e‘f x: QI/RN’)’ go dx: iroS/é)d% mad ijq/‘I’XLW c [ggﬂzaymmpaxzﬁde c '32uv‘3/9Jros‘160i9’; Lb‘f’ (A: (59/5J)I 5'0 9/14: —5,Q[9)6{9/ are/ 737F€1k3fé4 [031(5446' =.BJ‘[\$H(L{5)»[0SL{6J)€§,;‘[§))d? : Blffwzw)’ (>60;le FIRM,» 49 2 3%{64 - I) (A1 AA :: jlﬁm‘t—MZMK: 31 951451—3513) 7pc, : (of/94 ' gag/5) ’i’C/ WHMWWWMWWWWWW _ 2. [8 each] Evaluate each integral: a) /(2x+3)cos(5m) da: : (2X4—33u—5lzji’n (5,?) v— ;;R[fgp ).;1 Ax W k/~"’\/ W W W 4... 7‘ f) 13C 3 7 1“ 7x 3 = 6’: m(57a)—- 3; y m {52)olx 2 7”} Srk(5?)+ 3‘- (a [6?) + C, ' 6,, f S « W ﬁttwv. b) / COS4 sin3 dx zefcasqrx)(Fm‘kﬂénwﬂx =2 “‘[Mqﬂ'vd 4‘“ we'va 7’0 Ad (42mm, {0 WWW- li ’T‘Ca"”("‘f7fjl ,— @641 Mm WWMxWVWWWWW-“ﬁmvmmmwmmmwmmmm‘wmWKﬁ—m\w:vkww<ﬁkﬁ 3. [9 each] Evaluate each improper integral: 10 1 g a O , a) /2 m (1510 Impmldelf‘ «’1‘ x l S . l0 “L i ’0 % Chi) 34x 3 30(4); / 3 i (5) ’ E334) { f [6» 3WD H 04y :. 7}M Jed” 3:4 3 °°ln(:r) "‘4 W ‘9 15 b) /2 332 d”: [ﬁlﬁizdx 1": }ﬂ&)(’X—l)/’J:X’ll 01x 3’ z 2' .5 f __ “7"126) —z a ’}n6t + 1+" __ '74“) 7'0 1 71*? 1" ' ﬁz’ii’ 15 *1:th on A - ,Wﬂ 7 {L o 7N a :7m v—+LJ,.L ,1 ; J; AX x {#00[ ‘l’ 7’ '6 792 h( 7"(2)4/ ' 0+ 7‘33”) ’0 +3}. 3 2 / £400 ,7,\A['M' ’7W[M)g-7rm[i) “O + 2’ 1w 4" 19"” ’ if ' 1 4. [9] Sketch the region bounded by the curves y = g, y = 3:, y = 1 . Then use an integral or integrals to ﬁnd its area. m memwmmmeammmmmmmmWWWMNW““wwm\mwwxmwmtmmammw VMMMW u,“ A i M v, W; 4 M A i i D ‘ i g g 5. [9] Find the volume of the solid obtained by rotating the region . g bounded by y = 11:, y = 1, as = 4 (shown) about the y-axis. : q # (jam Miler: Gr @ﬂlC ) )A : ff“, 7. d g J l f ’9 3 I [K j ) 5L '1 § = ffléy-ﬁLfﬂ/I = 7T[(6‘1/ ‘ﬁkﬁéeiﬁ :79 5 l ‘7 .2 ('5 Mi “1 4 g uni 5 {ﬁrx (Xvi) Ax = 77' [th Ax : 217 [%x1ix‘7)ﬁ a l ' ’ l l i l i l l 6. [10] Sketch the region. bounded by y = 932 and a: + y = 2. Then ﬁnd the volume of the solid obtained by rotating this region about the x—axis. vext "W “I”? Zxﬁ;x amok: “xi—ea x7+x~1’°' 7—9 (ﬂak/«PO 73> x: —Q, I I UStV‘j/(MSb41/S“: V“: (Hf—[HJVAX x+g>a ’7. l : 7T ﬂq'ﬁx'} xqvx‘f)dx :: ﬁfty/1K7? éxa— 3531/ ’2, 'L 7. [8] SET UP, but do not evaluate, a deﬁnite integral that would give the volume of the solid obtained by rotating the region . bounded by x = y2 and g = 4 (shown) about the line y = 3. mﬁumm=ee§ﬂﬁwﬁaym]n< -‘IKmmmmmwﬁﬂwhﬁ\wﬁwaézm‘mwuw“:m®ﬁm\“mum‘thww‘mmmﬂwwmwmmu’xwrmwwmmwmwﬁwﬁww~mxnu l, L3 g 9 g 2 § 3 8. [2 per answer} Give a short answer for each question. No work or explanation necessary. a) To ﬁnd / sec5(\$) tan(a:) dry, one should use the substitution u = W063 2 . b) To ﬁnd / Vivi—f9— dm, one should use the substitution m = 3 56C (9) 113 - 6—“z . :3 ~ 6’” ’x_ —— doc IS convergent because — < X3 273 o) By the Comparison Theorem, / \$3 1 ‘forzc21. d) Write out the form of the partial fraction decomposition for each function. Do not determine the numerical values of the coefﬁcients A, B, etc. - —\$_ A Fr 13 1) \$2_2\$_3 7 4- >04 11 —————————-———-— z: ’1’ ) 332(952 + 2) X 4‘ X1 + {‘4 '3. w J, x1 ...
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## This note was uploaded on 03/30/2010 for the course MATH 172 taught by Professor Remaley during the Spring '10 term at Washington State University .

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172sP EXAM 1 SOLUTIONS - Math 172 ‘ EXAM 1 February 10,...

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