06pm1 - curves y 2 = x, x = 2 y about the y-axis. 5. Find...

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3B Practice Problems for Midterm I Spring 2006 Instructor: G. Wei The midterm will be from sections 4.10, 5.1-5.5, 6.1-6.2. Following are some practice problems. 1. Find the following integrals. (a) R e s cos( e s ) ds (b) R 1 0 e x 1+ e x dx (c) R 1 0 ( 4 u + 1) 2 du (d) R 2 0 t 1 + t 2 dt (e) R e x x dx (f) R tan x ln(cos 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 obtained by rotating the region bounded by y = x 2 , y 2 = x about the x -axis. 4. Find the volume of the solid generated by rotating the region bounded by the
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Unformatted text preview: curves y 2 = x, x = 2 y about the y-axis. 5. Find the derivative of the function. (a) f ( x ) = R x 1 1 + t 4 dt . (b) f ( x ) = R x 3 t 1+ t 3 dt . (c) f ( x ) = R 3 x +1 2 x sin( t 4 ) dt . 6. 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]....
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