Francisco Santos Nov 8, 2007
Practice Midterm 2
Name:
ID:
1.
(3 points each, 24 in total) Evaluate the following indeﬁnite integrals. Simplify your answers
as much as possible. Show your work. You may use
u
substitution, trig formulas, the
simple power rule, the fundamental theorem of calculus, integration by parts, partial
fraction decomposition, etc.
a.
R
(
x
+ 1)
e
x
2
+2
x

5
dx
=
b.
R
sec
10
x
tan
x dx
=
c.
R
ln
x dx
=
d.
R
xe

x
dx
=
e.
R
y
sin
y dy
=
f.
R
x

4
x
3
+
x
2
dx
=
2.
(3 points each, 6 in total) Evaluate the following deﬁnite integrals. Simplify your answers as
much as possible. Show your work. You may use
u
substitution, trig formulas, the simple
power rule, the fundamental theorem of calculus, integration by parts, partial fraction
decomposition, etc.
a.
R
2
0
x
(1

x
)
20
dx
=
b.
R
1
0
x
3
+10
x
+3
dx
=
3.
(5 points) Find the area of the region bounded by the graphs of
x
= 3
y
2
and
x
=

y
2
+ 4
y
.
Set up but DO NOT EVALUATE the integral(s).
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 Spring '11
 Smith
 Fundamental Theorem Of Calculus, University Honor Code, TRIG FORMULAS

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