05pm2

# 05pm2 - 5 If the work required to stretch a spring 1 ft...

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3B Practice Problems for Midterm II Winter 2005 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, 7.1-7.8. 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 + 0 e - 4 x dx (h) R 0 -∞ e x e x +1 dx 2. Use the Trapezoidal Rule and the Midpoint Rule to approximate the integral R 1 0 sin( x 2 ) dx with n = 4. 3. Find the volume of the solid obtained by rotating the region bounded by y = cos 2 x, 0 x π/ 2 about the y -axis. What about rotated about x -axis? 4. Does the integral R + 1 2+cos u u 2 du converge? Why or why not?
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Unformatted text preview: 5. 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? Optional: A coﬀee ﬁlter is in the shape of a inverted circular cone with radius 5 cm and height 10 cm. When it is ﬁlled with water to a height h cm, the rate at which coﬀee ﬂows out the hole at the bottom is given by h 2 cm 3 /sec. Suppose the coﬀee ﬁlter starts full. Find the time it takes for the coﬀee ﬁlter to empty....
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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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