Need help for calclus 2 exam.
MATH 201-01 Practice for Exam I
1. Indicate what method you will use to evaluate each integral, write down the right substitution you will use if it is a substitution method, without evaluating it.
a.
ò
-
dx
xe
x
2
b.ò
-
dx
xe
x
c.dx
x
x
ò
2
)
(ln
d.ò
xdx
x
ln
3
e.
ò
xdx
x
sin
f.ò
+
dx
x
x
3
1
g.ò
xdx
5
sin
h.ò
xdx
x
sec
tan
5
i.
ò
xdx
3
sec
j.dx
x
x
ò
-
4
2
k.dx
x
x
ò
-
2
2
4
l.dx
x
ò
+
2
2
)
1
(
1
m.
ò
-
+
dx
x
x
x
4
1
3
2. Evaluate each indefinite integral
a.
ò
dx
x
x
)
2
arcsin(
b.ò
dx
x
e
x
)
3
sin(
2
c.dx
x
ò
)
3
(
cos
4
d.ò
xdx
x
4
3
sec
tan
e.
dx
x
x
ò
-
9
2
f.ò
-
+
-
+
dx
x
x
x
x
x
1
2
2
3
2
g.dx
x
x
x
ò
+
+
2
2
3
)
1
(
4
3
3. Write the form of the partial fraction decomposition of the rational expression.
a.
x
x
x
x
x
4
4
4
3
2
3
2
+
-
+
+
b.)
2
(
)
1
(
1
2
2
3
2
3
+
+
+
+
x
x
x
x
x
4. Evaluate each definite integral
a.
ò
2
/
0
5
sin
p
xdx
b.ò
+
+
1
0
2
2
)
4
)(
1
(
1
dx
x
x
c.ò
-
1
0
2
/
5
2
)
1
(
dx
x
5. Evaluate each limit if it exists
a.
x
x
x
x
)
2
sin(
lim
0
+
®
b.2
0
)
1
(
lim
x
x
e
x
x
+
-
®
c.x
x
e
x
3
lim
¥
®
d.
x
x
x
ln
lim
0
+
®
e.)
1
(
lim
2
x
x
x
x
-
+
¥
®
f.n
n
n
)
2
1
1
(
lim
+
¥
®
6. Let
)
(
x
f
¢
¢
be continuous, find2
0
)
(
)
(
2
)
(
lim
h
h
x
f
x
f
h
x
f
h
-
+
-
+
®
.