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06m2-solution

# 06m2-solution - BB Midterm II Spring 2006 Instructor G Wei...

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Unformatted text preview: BB Midterm II Spring 2006 May 25, 06 Instructor: G. Wei Discussion time (circle one): W San: ; W 4pm; W 5pm; W 6pm; W 7pm Total Score: 100 Your Scores: 1‘ 2., ,. 3. ....... H 4. 5. Your Total You may have a 3 by 5 card but books and other notes are NOT allowed. Continue on the back of” the page if more space is needed READ the problems carefully No calcuiators are allowed. 1‘ (60 pts) Find the foilowing integrais‘ (a)\$55i11(:c2)d:13 (c) f 2 31112 :n (2033 mdcc . o 1r 5 go (Mil/X MLX 5935(5ng a: (ﬁx / a/crséosmf’ :g (/{1({’HL} phi X r . l 9,. w [a (M «r— M Ma. W ‘ 3 c: ' w <§- M -—-- 22"” M .., “L. M “'" 3 "cl: “‘9 W (3!) cos(3\$)ff;d_\$’ u— lv 1 H55 542x) ~—§%€,K('m?/Vj23 4% “I, W 3 " ’4‘ 2 6 Max) +3- e .{asx/[J56L’73zdzxp/j ww- 3 LX J 2, a mu) +3; 1rnew~r£felwxw 2" (10 pts) Find the average value of the function ﬁt) m 155111052) 011 the intezval [0,101‘ 3. {15 pts) A force of 30 N is required to maintain a spring stretched from its nature} length of 12 cm to a iength of 15 cm How much work is done in stretching the spl'ing from 12 cm to 20 can? fka ,_ WW X 4% a; WV’MJ {’6 S#%/M" wlm X7{/§'—/Z)0’m eBM 2" 0.05m flaw/y 4‘ (15 pts) Find the volumes of the solids obtained by Iotating the region bounded by 'y = sin 3, 3: = 7r/2, :1: = 7r, y = 0 about the xwalxis and y—axis respectively. ...
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