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Unformatted text preview: Instructor: Prof. Wei 1. Find the following integrals. (a) R e s cos( e s ) ds (b) R 1 4 x 3 x 2 +4 dx . (c) R 1 ( 4 u + 1) 2 du . (d) R e x x dx . 2. Find the area of the region enclosed by the line y=x-1 and the parabola y 2 =-2 x + 5. 3. Find the volume of the solid generated by rotating the region bounded by the curves y 2 = x,x = 2 y about the y-axis. Sketch the region, the solid, and a typical disk or washer. 4. Find the derivative of the function. (a) f ( x ) = R x 3 t 1+ t 3 dt . (b) f ( x ) = R 3 x +1 2 x sin( t 4 ) dt . 5. A particle moves along a line with velocity function v ( t ) = t 2-t-12, where v is measured in meters per second. Find (a) the displacement and (b) the distance traveled by the particle during the time interval [1 , 6]. 1...
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- Fall '07