Name: ________________________ Class: ___________________ Date: __________ ID: A
Midterm 1: February 13, 2008
Free Response
y
= 4 -
x
y
=
x
- 2
1. Sketch the region enclosed by and . Decide whether to integrate with respect to
x
or
y
.
2 2
Find the area of the region.
= =
y
x
y
x
2. Find the volume of the solid obtained by rotating the region bounded by and about the line
= 0
y
.
(
x
) = 8
3. The linear density of a 15 m long rod is kg/m, where
x
is measured in meters from one end o
f
(3 +
x
)2
the rod. Find the average density of the rod.
4. Use the method of cylindrical shells to find the volume of a solid obtained by rotating the region bounded by
the given curves about the
y
axis.
= 3 -
y
x
x
,y= 0
2
Multiple Choice
I
dentify the choice that best completes the statement or answers the question.
_
___ 5. A spring has a natural length of 22 cm. If a force of 15 N is required to keep it stretched to a length of 32 cm,
how much work is required to stretch it from 22 cm to 40 cm? Force to pull spring is given by
-
F
(
x
) = k (
x
x
)
0
Select the correct answer.
a. 3.43 J
b. 1.93 J
c. 2.93 J
d. 3.93 J
e. 2.43 J
1
