Final Exam
(Mock Test)
Math 12010-003
Answer the cluestions in the spaces provided. Show all of your work.
Name:
ID: U
0
Question:
1
2
3
4
5
6
7
8
9
10
11
Total
Points:
10
10
10
10
10
10
10
5
10
10
5
100
Score:
1. For each of the following problems sketch the region R, shade it and calculate the area.
(a)
5 points Region bounded by y =
y = 0 ..‘r = —8 aind r = 8.
(b) [points Region bounded by x
I
i
C
/
=
4/ arid
x
=
8
— 4y
.
1
‘!
(
1
.L
2.
rfüi)oilIts
Find the voliune of the solid generated by revolving the region R bounded
h y
=
0,
:i:
=
2
4, about the
uid 2
:r-axis.
(Sketch tlw region first and shade
it).
j
2
3.
10 points Find the volume of the solid generated by revolvuig the region R hounded
by y 6i afl(l II = 612, about the .x-axis. (Sketch the region first and shade it).
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cy
( )k -\) L\J
r.(
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—
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/
,y
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—)--
u
.—
-
Page 2
4. points Find the volume of the solid generated by revolving the region R in the first
quadrant bounded by y =
y = 2 — .2 and r 0. about. the il-axis. (Sketch the legion
first and sun de it.)
t.
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5.
(a)
5 points] Find the length of the arc y
=
\_(.)\
d’
_j
2 + 1)3/2 between
(:r
=
1 and x
=
—
—-
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