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Math 252, Fall 2004
NAME (print) _________
KEY
__________________________
Scarborough
Final Exam
NAME (sign) ________________________________________
Student Number ______________________________________
This exam is closed book. Notes are not allowed.
A Calculator is required.
Calculators may only be used to plot graphs and for numerical calculations.
The advanced symbolic features of some calculators may not be used on this exam and such
answers will not be accepted.
For full credit show all work.
Part of the grading will be based on proper use of notation.
This exam has 9 pages with 11 problems. You should scan all the problems before you begin the test so
you can plan out your time. The time limit on this exam is 1 hour 50 minutes.
If more room is needed please use the back of the pages.
You may find the following formulas of interest:
±
x
=
b
²
a
n
x
i
=
a
+
i
±
x
R
n
=
f
(
x
0
)
+
f
(
x
2
)
+
f
(
x
3
)
+
±
+
f
(
x
n
±
1
)
[]
²
x
L
n
=
f
(
x
1
)
+
f
(
x
2
)
+
f
(
x
3
)
+
±
+
f
(
x
n
)
±
x
M
n
=
f
x
0
+
x
1
2
±
²
³
´
µ
¶
+
f
x
1
+
x
2
2
±
²
³
´
µ
¶
+
f
x
2
+
x
3
2
±
²
³
´
µ
¶
+
±
+
f
x
n
·
1
+
x
n
2
±
²
³
´
µ
¶
¸
¹
º
»
¼
½
¾
x
T
n
=
1
2
f
(
x
0
)
+
2
f
(
x
1
)
+
2
f
(
x
2
)
+
±
+
2
f
(
x
n
²
1
)
+
f
(
x
n
)
±
x
E
M
n
±
K
(
b
²
a
)
3
24
n
2
and
E
T
n
±
K
(
b
²
a
)
3
12
n
2
where
³³
f
(
x
)
±
K
for
a
±
x
±
b
S
n
=
1
3
f
(
x
0
)
+
4
f
(
x
1
)
+
2
f
(
x
2
)
+
4
f
(
x
3
)
+
±
+
2
f
(
x
n
±
2
)
+
4
f
(
x
n
±
1
)
+
f
(
x
n
)
²
x
where
n
is even
E
S
n
±
K
(
b
²
a
)
5
180
n
4
where
f
(4)
(
x
)
±
K
for
a
±
x
±
b
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View Full Document Math 252, Fall 2004
Final Exam
Page 2
1.
Consider the region enclosed between the curves
y
=
2
x
and
y
=
x
2
.
( a )
Draw a picture of this region.
( 1 pt )
( b ) Set up the integral that describes the area of this region
( 2 pt )
2
x
±
x
2
()
dx
0
2
²
( c )  Evaluate this integral.
( 1 pt )
2
x
±
x
2
dx
0
2
²
=
x
2
±
x
3
3
2
0
=
4
±
8
3
=
4
3
( d )
Set up the integral for
M
x
for this region.
( 1 pts )
1
2
(2
x
)
2
±
x
2
2
dx
0
2
²
( e )  Evaluate this integral
( 1 pt )
1
2
(2
x
)
2
±
x
2
2
dx
0
2
²
=
1
2
4
x
2
±
x
4
dx
0
2
²
=
2
x
3
3
±
x
5
10
2
0
=
16
3
±
16
5
=
32
15
( f )
Set up the integral for
M
y
for this region.
( 1 pts )
x
2
x
±
x
2
dx
0
2
²
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This note was uploaded on 03/15/2009 for the course MTH 252 taught by Professor Smith during the Spring '08 term at Oregon State.
 Spring '08
 SMITH
 Math

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