MATH 129
FINAL EXAM REVIEW PACKET
(Revised Fall 2010)
The following questions can be used as a review for Math 129. These questions are not actual
samples of questions that will appear on the final exam, but they will provide additional practice
for the material that will be covered on the final exam. When solving these problems keep the
following in mind: Full credit for correct answers will only be awarded if all work is shown.
Exact values must be given unless an approximation is required. Credit will not be given for an
approximation when an exact value can be found by techniques covered in the course. The
answers, along with comments, are posted as a separate file on http://math.arizona.edu/~calc.
1. Suppose the rate at which people get a particular disease (measured in people per month) can
be modeled by
( )
10
sin
30
3
r t
t
π
π
=
+
. Find the total number of people who will get the disease
during the first three months (
0
3
t
≤
≤
).
2. If
3
1
( )
7
f u du
=
∫
, find the value of
2
1
(5
2 )
f
x dx
−
∫
.
3. Evaluate
1
t
dt
t
+
∫
4. Use the method of integration by parts:
a) Evaluate
(
)
2
2
ln
1
z
dz
z
+
∫
b)
Evaluate
2
arcsin(
)
x
x
dx
∫
.
c)
Let
g
be twice differentiable with
(0)
6
g
=
,
(1)
5
g
=
,
and
(1)
2
g
′
=
. Find
1
0
( )
x g
x dx
′′
⋅
∫
.
5. Evaluate the following integrals (you can use the table of integrals):
a)
2
cos (3
2)
d
θ
θ
+
∫
b)
2
2
4
9
dt
t
−
∫
c)
2
8
15
dy
y
y
+
+
∫
6. Use the method of partial fractions to evaluate
3
3
3
5
1
y
y
dy
y
y
+
−
+
∫
.

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*