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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 6.36.5, 7.17.5.
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 yaxis. What about rotated about xaxis? 4. If the work required to stretch a spring 1 ft beyond its natural length is 12 ftlb, 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.
 Fall '07
 RickRugangYe
 Integrals

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