102-2005&2006-3-M20-July2006

102-2005&2006-3-M20-July2006 - , Kuwait University...

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, •Kuwait University Dept of Math Comp Sci Math 102 Second Examination July 17, 2006 Duration: 90 minutes The use of calculator is not allowed. Turn off your mobile phone or pager 1. Evaluate the following integrals. ~ (a) J _~__ X=5,------=_ dx V 1 - :r:3 (3 points each) ~ (b) J J x2 - 2x - 8 x-I dx -3 (d) J ~X2 - x + 2 dx '3 (e) J 2+U:m~ _ dx o 2. Determine if the improper integral J eX dx is convergent or divergent, and find its value VI + e-2x -CD if it is convergent. *2_ 3. Find the length of the arc of f(x) = In(secx), 0 ~ x ~ ~. (3 points) (2 points) 2--- 4. Find the surface area of the solid obtained by revolving the curve f(x) = cosh x, 0 ~ x ~ 1 about the y-axis. (2 points)
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'L . ' J ~t ~t(.( ::: ) (u - ) -t- ~ ) d LA- :- ~ 2 - L( I y", ! u-rl(t ~ ~ ~ l 2 f3 ,,?' () I ! ;>" \ ( = -;: (3 -x - i) _ C 3 h- i) --l Y 1'\ (:;Sir -I) -t- I '\ '--- ,J Co '3)( __ I = U -I. . '2 =-:::> C'X d)( =- 3 u.. d t-{ :::: ::>)( d )' ~ L{ c) L( " ~J~2_7X 3 . K I :3<;(' (D cJ)( .:),5,' (LQ (c.-I.' p.,1 l-r-e
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102-2005&amp;amp;2006-3-M20-July2006 - , Kuwait University...

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