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Stewart_Calc_7ET ch06sec05
MULTIPLE CHOICE
1. The linear density of a m long rod is
where x is measured in meters from one end of the rod. Find the average density of the rod.
a.
b.
c.
d.
e.
2. In a certain city the temperature hours after 7 A.M. was modeled by the function
Find the average temperature to three decimal places during the period from 7 A.M. to 7
P.M.
a.
b.
c.
d.
e.
3. Find the average value of the function on the given interval.
a.
b.
c.
d.
e.
4. Find the average value of the function on the interval . Round your
answer to 3 decimal places.
a.
9.342
b.
0.45
c.
0.432
d.
e.
18
5. The temperature of a metal rod, m long, is x (in degree Celsius) at a distance x meters
from one end of the rod. What is the average temperature of the rod?
a.
b.
c.
d.
e.
6. Find the average value of the function on the interval .
a.
b.
c.
d.
e.
MULTIPLE RESPONSE
1. Find the number(s) a such that the average value of the function on
the interval is equal to 10.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Find the average value of the function on the given interval.
2. Find the number(s) a such that the average value of the function on the
interval is equal to .
3. True or False?
The Mean Value Theorem for Integrals says that if is continuous on [ , ], then there
exists a number m in [ , ] such that
4. The velocity v of blood that flows in a blood vessel with radius and length l at a distance
from the central axis is
where P is the pressure difference between the ends of the vessel and q is the viscosity of
the blood. Find the average velocity (with respect to r) over the interval
5. Find the average value of the function on the interval .
SHORT ANSWER
1. Find the volume of the solid obtained by revolving the region under the graph of
on [1, ) about the x-axis.
