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Unformatted text preview: 3B Practice Problems for Final Winter 2005 The ﬁnal is on Monday, March 14, 7:30 – 10:30pm at EMBAR Hall You may bring
a 3 by 5 card.
I will have extra oﬃce hour on 3/14, Monday 911am at SH 6503.
The ﬁnal will be from sections 5.15.5, 6.16.5, 7.17.8, 8.18.3 and 10.110.4.
Subjects you need to know well and use well:
The fundamental theorem of calculus, basic integration formulas, substitution
rule, integration by parts, integration of trig functions, rational functions, improper
integral.
Application of integration to distance, area, volume, work, arc length, surface
area, center of mass; parametric curves.
A good starting point for preparing the ﬁnal is doing the problems from previous
practice and midterms.
Following are some more practice problems.
5x
1. Find the derivative of the function y = cos x cos(u2 )du.
2. Find the following integrals.
(a) es cos(es )ds (b) 01 (e − ex )x dx
√
2
(c) lnx x dx
t2
(d) 02 t 1 + √ dt
2
(e) sin(3x)e2x dx
(f) 12 xx−1 dx
1
(g) sin2 x cos3 xdx
(h) x2 +4x+8 dx
1
(i) x2 +5x−6 dx
(j) x2 −61x+10 dx
(k) 01 x ln xdx
x2
(l) Is 1+∞ √x2 +3+1+7x7 dx convergent or divergent?
3
x3
3. A 1000lb cube of ice must be lifted 50 ft, and it is melting at a rate of 2 lb
per minute. Assume that it can be lifted at a rate of one foot every minute. Find the
work needed to get the block of ice to the desired height.
4. a) Find the length of the curve
x
√
t − 1dt 1 ≤ x ≤ 16
y=
1 b) Find the area of the surface obtained by rotating this curve about yaxis.
5. Find the centroid of the region bounded by the curves y = 4 − x2 , y = x + 2.
6. Determine the volume of the solid obtained by rotating the region bounded by
the function f (x) = ex/3 , the lines x = 0, x = 1 and the xaxis around the line y = 4.
7. Chapter 10 concentrate on the HW problems. ...
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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.
 Fall '07
 RickRugangYe

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