Test 2 Practice Problems
I suggest looking over the Test 2 Review sheet before attempting these problems.
It will help you get a better feel for what you know and what you need to work on.
•
Area Between Curves
1. Find the area between the curve
y
= 1
/x
and the
x
axis from
x
= 1 to
x
= 2.
2. Find the area of the ”triangular” region bounded on the left by
x
+
y
= 2,
on the right by
y
=
x
2
, and above by
y
= 2.
3. Find the area between
f
(
x
) =
x
3

3
x
2
and the
x
axis.
4. Find the area between
x
= 4

y
2
and
x
= 0.
5. Find the area of the ”triangular” region bounded on the left by
y
=
√
x
,
on the right by
y
= 6

x
, and below by
y
= 1.
6.
You absolutely want to know how to do the last problem on the
5.7 Worksheet
.
Make sure you understand how to deal with regions
that have two different functions bounding them on one side.
•
CrossSectional Volumes
Find the volume of the following solids.
1. The solid lies between planes perpendicular to the
x
axis at
x
=

1 and
x
= 1. The crosssections perpendicular to the
x
axis are circular disks
whose diameters run from the parabola
y
=
x
2
to the parabola
y
= 2

x
2
.
2. The solid lies between planes perpendicular to the
x
axis at
x
=

1 and
x
= 1. The crosssections perpendicular to the
x
axis between these planes
are squares whose diagonals run from the semicircle
y
=

√
1

x
2
to the
semicircle
y
=
√
1

x
2
.
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 Spring '08
 LLHanks
 Calculus, Region, xaxis

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