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Name: __________________
Class:
Date: _____________
(First Page)
Name: __________________
Class:
Date: _____________
(Subsequent Pages)
1.
Find the average value of the function on the given interval. Reduce your answer to lowest terms.
, [0, 8]
2.
The region bounded by the curve
,
is rotated about the axis
. Find the volume of the resulting solid by any method.
3.
Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the curve
,
about the axis
,
;
.
a.
b.
c.
d.
e.
4.
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves
,
about the x-axis.
5.
Find the values of c such that the area of the region bounded by the parabolas
and
is 1944.
________
6.
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Refer to the figure and find the volume generated by rotating the
about
.
Enter your answer as an expression using the symbol
or as a decimal rounded to the nearest hundredth.
7.
Refer to the figure and find the volume generated by rotating the given region about the specified line.
about
Enter your answer as an expression using the symbol
8.
Find the average value of f on the given interval.
or as a decimal rounded to the nearest hundredths.
,
9.
Find all number(s) b such that the average value of
10.
Find the area of the region bounded by the curves
on the interval [ 0, b ] is equal to 8.
,
,
, and
.
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ANSWER KEY
HW #1
1
2
3d
4
5
6
7
8
9
10
ANSWER KEY - Page 1
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