102-2006&2007-2-F11-June2006 - Math 102 Calculus II...

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102, Calculus II Final Exam. Date: 01/06/2006 Duration: 2 hours. Answer all questions. Calculators and Mobile Phones are not allowed. 1. (4pts.) (a) Find the exact value of sin(tan-I(~)). (b) Find the exact value of coth(ln 2). 2. (4pts.) Let f(x) = fox tan(t) sec2(t)dt,O < x < 11/2. Find (a) f'(x) (b) f(1I/4) (c) (f-IY(~). 3. (12pts.) Find, if possible, (a) / tan~l x dx (b) jIlnx dx OJi 2 X (c) h ~ ~ d.'L 4. (4pts.) A curve C is given parametrically by x = (t2 + l)et and y (t3 + 2t2)et. (a) Find the points P (.'L, y) where the tangent is vertical. (b) Determine whether.C is concaveypw!1rds. or downwards at t .0. J. (4pts.) Find the area of the surface obtained by rotating the curve y = Jx + 1, 1 < x < 5 about the x-axis. 6. (4pts.) Find the centroid (center of mass) of the region bounded by the . 0 'if d 3 'if curves y = SIn x, y = , x = "4an x = 4' 7. (4pts.) Find the length of the curve T = 4 cos2(~). 8. (4pts.)
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102-2006&amp;2007-2-F11-June2006 - Math 102 Calculus II...

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