06pm2 - , 2]. 3. Find the volume of the solid obtained by...

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3B Practice Problems for Midterm II Spring 2006 Instructor: G. Wei You may bring a 3 by 5 inch card to the second midterm, which will be from sections 6.3-6.5, 7.1-7.5. Following are some practice problems. 1. Find the following integrals. (a) R e 1 ln( x 4 ) dx (b) R x 5 e x 2 dx (c) R π/ 2 0 cos 3 t sin 4 t dt (d) R ( e - 2 x sin 2 x ) dx (e) R x 2 +8 x - 3 x 3 +3 x 2 dx (f) R 2 / 2 0 x 2 1 - x 2 dx (g) R sin 3 x cos 7 xdx 2. Find the average value of the function f ( x ) = 2 x/ (1+ x 2 ) 2 on the interval [0
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Unformatted text preview: , 2]. 3. Find the volume of the solid obtained by rotating the region bounded by y = cos 2 x, ≤ x ≤ π/ 2 about the y-axis. What about rotated about x-axis? 4. If the work required to stretch a spring 1 ft beyond its natural length is 12 ft-lb, how much work is needed to stretch it 9 in beyond its natural length?...
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This note was uploaded on 12/27/2011 for the course MATH 5B taught by Professor Rickrugangye during the Fall '07 term at UCSB.

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