172 FALL 2009 EXAM 1 SOLUTIONS

172 FALL 2009 EXAM 1 SOLUTIONS - SE g a g i Math 172...

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Unformatted text preview: SE g a g i § § 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 “I: x mZ—x—Z / gx~2xx~H> flax ‘X .. fl . B ( -— m ‘ N X~H beam-e 0 Let _ «>02 (K: AQWH-x) +ECV~Z) x: wewa + A~2~B smmrmuxwxm¢m&aquWfifiWWWEWWKXMWEWWWmm‘mmwmumwmmxmwmwAhmWimmflwmumxxox>\m\kerwnmqvmwwwmn<mmu (b) / v 1 — x2 dx. Hint: Consider a substitution: 3: = sin 6. (c) / sin3 3: cos an den M a f +8, M“ i a U =— SMX' 2. (10 pts each) Evaluate each of the following improper integrals: (Hint: A limit relationship?) ‘ “== ewcwww lo :— fimft3(3“-M““gf>+—l] {7%(3’0 1 (b) fgjll—fldx ° . l «v 21M; timlw W {-9 or +30" ) Q V9, l A ‘ QU‘xl? §£$+<19< "/%::;o’f :‘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: Hooke’s law: f = kx.) E a] g «WMWWNWWWWmmflmwmmmmw, \ 5 4. (10 pts) Find the area bounded between the curves y = fl and y = x2. =>< \3 Wfi:/)(l. (XEXSC PKV~’X:5. “X3(><v~\) 315’ - :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 = fl and y = :32 about the x—axis. Ba me's WWI : V :. Trftfx')l- (93);] 61X 7 5,: cx~ X‘LBJX in? 5 '5‘ '2‘. [£%~§~fi§x >le “MET? " ’FS‘ or B? Ska/H‘s WWJ "QW‘3L(J§~ “Sufi? :QJK “$%¥> 0 ._ 1E 6. (10 pts) Use the method of cylindrical shells to find the volume of the solid generated by rotating the region bounded by the curves ‘5: X} y = fl and y = 2:2 about the y—axis. V c: 5Jam<U7<~Xl> (XX ‘1 301’“ QWB/iwévw :QT(%X§/zm fix?) 7. (10 pts) Find the length of the curve: y = — 2)3/2, 3 g m S 4. l & o ...
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