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Math 20B
Second Exam (125 points)
4:40 PM
March 5, 2001
•
Please put your name, ID number, and section number (or time) on your blue book.
•
The exam is CLOSED BOOK, but you may use ONE SHEET OF NOTES.
•
Calculators are NOT allowed.
•
You must show your work to receive credit.
1. (80 pts.) Evaluate the following integrals. Remember to show your work!
(a)
Z
1
/
2
0
x
√
1

x
2
dx
(b)
Z
√
t
‡
t
+
3
√
t
·
dt
(c)
Z
sin
2
t
cos
3
tdt
(d)
Z
(ln
x
)
2
dx
(e)
Z
1

1
1
x
3
dx
2. (15 pts.) Set up the integral for the volume of the solid obtained by rotating the
region bounded by
y
=0
,y
= sin
x,
0
≤
x
≤
π
about the line
y
=1.
Your answer should include a sketch of the region together
with the line about which the region is being rotated.
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This note was uploaded on 06/17/2009 for the course MATH 20B taught by Professor Justin during the Winter '08 term at UCSD.
 Winter '08
 Justin
 Math, Calculus

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