Test 2 Review
Test 2 is a freeresponse, no calculator exam. It is scored out of 50 pts. It will be
given IN CLASS on Monday, March 17, 2008.
What does Test 2 cover?
5.6 Areas Between Curves
5.7 The Logarithm Defined as an Integral
6.1 Crosssectional Area and the Disk
\
Washer Method
6.2 The Shell Method
6.3 Curve Length
6.6 Work
6.7 Moment and Center of Mass
Note: Even though we are not specifically covering material from Test 1, you will be
responsible for knowing how to use integration techniques that were introduced in
those sections (i.e. antiderivative rules and usubstitution)
The following is an outline on what you should DEFINITELY know for the test.
Areas Between Curves (5.6)
•
Know the area formulas and how to use them:
If
f
(
x
)
≥
g
(
x
) on [
a, b
] then
A
=
b
a
[
top

bottom
]
dx
=
b
a
[
f
(
x
)

g
(
x
)]
dx
.
If
f
(
y
)
≥
g
(
y
) on [
c, d
] then
A
=
d
c
[
right

left
]
dy
=
d
c
[
f
(
y
)

g
(
y
)]
dy
.
•
Understand how to integrate with respect to both
x
and
y
:
Integration with respect to x  the only variables seen in the integrand should
be
x
’s. Make sure all functions are written in terms of y = f(x). The bounds
on the integral should be
x
values.
1
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Integration with respect to y  the only variables seen in the integrand should
be
y
’s (No
x
’s!!). Make sure all functions are written in terms of x = f(y). The
bounds on the integral should be
y
values.
•
If bounds are not given in the problem statement, you are to assume that
the bounds come from the intersection points of the functions that bound the
region. You will need to find these.
•
Steps to follow when finding the area between curves:
1. Sketch a quick graph of your region. Identify all intersection points and
bounds on your region. Make sure that the region you have selected does
indeed touch each of the given bounding functions.
2. Determine which variable you want to integrate with respect to.
Your
ability to rearrange functions into the form x = f(y) and y = f(x) should
help you determine which variable to use.
3. Identify which function is on top (for
x
integration) or which is on the
right (for
y
integration).
Intersection points are the only places where
functions can switch between which is on top
\
bottom or right
\
left. Test
points in the intervals between the intersection points to accomplish this
goal.
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 Spring '08
 LLHanks
 Calculus, Disk Method, Center Of Mass, Region

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