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Unformatted text preview: y being sin( y ) and cos( y ). 4. (20 points) Find the surface area of the surface obtained by rotating the parameterized curve with x ( t ) = 1 + sin( t 2 ) and y ( t ) = 1 + cos( t 2 ) for t ∈ [0 , √ 2 π ] about the y axis. 5. (20 points) It requires half as much work to pull the end of a spring from 2 inches to 3 inches extenion as it does to pull it the next inch (from 3 inches to 4 inches extension). How many inches extended is the rest position of the spring? 6. (20 poimts) Find x ( t ) if ( t + 1) dx dt = x 2 + 1 with the initial condition that x (0) = 0. 7. (30 points) Find the following numbers: (a) d dx i t = x t =1 et 2 dt at x = 0 (b) i x = ∞ x =1 2 dx x 2 + x (c) i x =1 x =0 √ xe √ x dx 8. (30 points) Find the following families of functions: (a) i dx x (ln( x )) 2 if x > (b) i x 2 dx ( x 21) 5 2 if x > 1 (c) i r 1cos( x ) dx...
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 Spring '06
 Sarason
 Math, Calculus, ........., Isotope

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