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Â§ Math 172 Exam #1 Name: Section#: Signature:___________________ ID# September 29, 2009 Instructions: Do all the problems. Circle your answers. To get credit,
you need to show your work. The answer alone will not be. counted as a solution. 1. (10 pts each) Evaluate each of the following integrals: (a) / x (136 â€œI: x mZâ€”xâ€”Z / gx~2xx~H> ï¬‚ax
â€˜X .. fl . B (
â€” m â€˜ N X~H beame 0 Let _
Â«>02 (K: AQWHx) +ECV~Z)
x: wewa + A~2~B smmrmuxwxmÂ¢m&aquWï¬ï¬WWWEWWKXMWEWWWmmâ€˜mmwmumwmmxmwmwAhmWimmï¬‚wmumxxox>\m\kerwnmqvmwwwmn<mmu (b) / v 1 â€” x2 dx. Hint: Consider a substitution: 3: = sin 6. (c) / sin3 3: cos an den M a f +8, Mâ€œ
i a U =â€” SMX' 2. (10 pts each) Evaluate each of the following improper integrals:
(Hint: A limit relationship?) â€˜ â€œ== ewcwww lo
:â€” ï¬mft3(3â€œMâ€œâ€œgf>+â€”l]
{7%(3â€™0 1 (b) fgjllâ€”ï¬‚dx Â° . l Â«v
21M; timlw W {9 or +30" )
Q V9, l A â€˜ QUâ€˜xl?
Â§Â£$+<19< "/%::;oâ€™f :â€˜gl 3. (10pts) A force of 10 N is required to maintain a spring stretched from
its natural length of 1m to a length of 2m: How much work is done in
stretching the spring from 2m to 3m? (Hint: Hookeâ€™s law: f = kx.) E
a]
g Â«WMWWNWWWWmmï¬‚mwmmmmw, \ 5 4. (10 pts) Find the area bounded between the curves y = ï¬‚ and y = x2. =><
\3 Wï¬:/)(l. (XEXSC
PKV~â€™X:5. â€œX3(><v~\) 315â€™ 
:v . [Kilf " XS/zw ELXB>L9
\\ MO 2% 5. (10 pts) Find the volume of the solid generated by rotating the region
bounded by the curves y = ï¬‚ and y = :32 about the xâ€”axis. Ba me's WWI :
V :. Trftfx')l (93);] 61X
7 5,: cx~ Xâ€˜LBJX in? 5 '5â€˜
'2â€˜. [Â£%~Â§~fiÂ§x >le
â€œMET?
" â€™FSâ€˜
or B? Ska/Hâ€˜s WWJ
"QWâ€˜3L(JÂ§~ â€œSuï¬? :QJK â€œ$%Â¥> 0
._ 1E 6. (10 pts) Use the method of cylindrical shells to ï¬nd the volume of the solid generated by rotating the region bounded by the curves
â€˜5: X} y = ï¬‚ and y = 2:2 about the yâ€”axis. V c: 5Jam<U7<~Xl> (XX
â€˜1 301â€™â€œ QWB/iwÃ©vw :QT(%XÂ§/zm ï¬x?) 7. (10 pts) Find the length of the curve: y = â€” 2)3/2, 3 g m S 4. l
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 Spring '10
 REMALEY
 pts, Riemann integral, following improper integrals

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