Multiple Choice Identify the
choice that best completes the statement or answers the question.


1.

Find the indefinite integral.


2.

Find the indefinite integral.


3.

Find the indefinite integral.


4.

Find the indefinite integral.


5.

Find the indefinite integral. Hint:


6.

Find the indefinite integral.


7.

Find the indefinite integral.


8.

Find f( x) by solving the initial value problem.


9.

Find f( x) by solving the initial value problem.


10.

Lorimar Watch Company manufactures travel clocks. The daily marginal cost
function associated with producing these clocks is where
C '( x) is measured in dollars/unit and x denotes the number of units
produced. Management has determined that the daily fixed cost incurred in producing these clocks is
$170. Find the total cost incurred by Lorimar in producing the first 400 travel clocks/day.
A  $3,566  B  $3,354  C  $3,282  D  $3,485 


11.

The temperature on a certain day as measured at the airport of a city is
changing at the rate of , where is measured in hours, with corresponding to 6 a.m. The temperature at 6
a.m. was . What was the temperature at 9 a.m.? Please
round your answer to whole degrees.


12.

The velocity, in feet/second, of a rocket t seconds into vertical flight
is given by What is the altitude of the rocket 40
seconds after liftoff? Hint:
A  89,200 ft  B  88,900 ft  C  89,400
ft  D  89,100 ft 


13.

Find an approximation of the area of the region R under the graph
of f by computing the Riemann sum of f corresponding to the partition of
the interval into the subintervals shown in the accompanying figures. Use the midpoints of the
subintervals as the representative points. Round your answer to the nearest hundredth.
A  1.92 sq units  B  0.85 sq units  C  2.34 sq
units  D  2.27 sq units 


14.

Let f(x) = 4x
Sketch the region R under the
graph of f on the interval [0, 2] and find its exact area using geometry.
A  8 sq units;
 C  10 sq units;
 B  8 sq
units;
 D  10 sq units;



15.

Let f(x) = 8x
Use a Riemann sum with four
subintervals of equal length (n = 4) to approximate the area of R (under the graph
of f on the interval [0, 2]). Choose the representative points to be the left
end points of the subintervals.
Repeat previous part with eight subintervals of equal length
(n = 8).
Compare the approximations obtained in previous parts with the exact area (16
sq units). Do the approximations improve with larger n?
A  12 sq units; 14 sq units; no  B  12 sq units; 14 sq units;
yes  C  14 sq units; 12 sq units; no  D  14 sq units; 12 sq units;
yes 


16.

Let and compute the Riemann sum of f over
the interval , choosing the representative points to be the
midpoints of the subintervals, using five subintervals of equal length ( ).
A  12.3325 sq units  B  15 sq units  C  12.33 sq
units  D  11 sq units  E  12.3125 sq units 


17.

Let and compute the Riemann sum of f over
the interval [2, 4] , using Two subintervals of equal length ( n = 2).
Five subintervals of equal length ( n = 5). Ten subintervals of equal length
( n = 10). In each case, choose the representative points to be the right end points of
the subintervals.
A  100 sq units; 84.48 sq units; 79.52 sq units;  B  79.52 sq units; 84.48
sq units; 100 sq units;  C  100 sq units; 79.52 sq units; 84.48 sq
units;  D  84.48 sq units; 79.52 sq units; 100 sq units; 


18.

Find an approximation of the area of the region R under the graph of the
function f on the interval [ a, b]. Use n subintervals and
choose the representative points as indicated.
A  1.77 sq units;  B  1.54 sq units;  C  1.4 sq
units;  D  1.9 sq units; 


19.

Find the area of the region under the graph of the function on the interval , using the fundamental theorem of calculus.
Then verify your result using geometry.


20.

Find the area of the region under the graph of the function on the interval .


21.

Find the area of the region under the graph of the function on the interval .


22.

Evaluate the definite integral.


23.

Evaluate the definite integral.


24.

Find the area of the shaded region.
A  A = 21.3 sq units.  B  A = 19.9 sq units.  C  A = 18.1 sq
units.  D  A = 23.6 sq units. 


25.

Find the area of the shaded region.
A  A = 13 sq units.  B  A = 9 sq units.  C  A = 12 sq
units.  D  A = 10 sq units. 


26.

Sketch the graphs of the functions f and g and find the area of
the region enclosed by these graphs and the vertical lines x = a and x =
b.


27.

Find the area of the region enclosed by these graphs and the vertical lines and .


28.

Sketch the graph and find the area of the region completely enclosed by the
graphs of the given functions f and g.


29.

The demand function for a certain make of replacement cartridges for a water
purifier is given by where p is the unit price in
dollars and x is the quantity demanded each week, measured in units of a thousand. Determine
the consumers' surplus if the market price is set at $5/cartridge. Round your answer to the
nearest dollar.
A  $16,886  B  $16,800  C  $16,333  D  $16,667 


30.

The demand function for a certain brand of compact disc is given by The supply function for the compact discs of is given by where p is the wholesale unit price in dollars and x is the quantity
demanded each week, measured in units of a thousand. Determine the producers' surplus if the
wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.
A  $11,894  B  $11,792  C  $11,346  D  $11,667 


31.

The management of the Titan Tire Company has determined that the quantity
demanded x of their Super Titan tires/week is related to the unit price p by the
relation where p is measured in dollars
and x is measured in units of a thousand. Titan will make x units of the tires
available in the market if the unit price is dollars. Determine
the consumers' surplus and the producers' surplus when the market unit price is set at the
equilibrium price. Round your answers to the nearest dollar.
A  CS = $337,012 , PS = $174,988  B  CS = $343,476
, PS = $168,524  C  CS = $341,333 , PS =
$170,667  D  CS = $342,567 , PS = $169,433 


32.

Find . Round your answer to the nearest integer.
A  1,619,649  B  1,607,304  C  1,622,538  D  1,562,181 

Numeric Response


33.

Annual sales (in millions of units) of handheld computers are expected to grow
in accordance with the function where t is measured in years,
with t = 0 corresponding to 1997. How many handheld computers will be sold over the 6year
period between the beginning of 1997 and the end of 2002? Round your answer to two decimal
places, if necessary.


34.

The demand function for a certain brand of compact disc is given by The supply function for the compact discs is given by where p is the wholesale unit price in dollars and x is the quantity
demanded each week, measured in units of a thousand. Determine the producers' surplus if the
wholesale market price is set at the equilibrium price. Round your answer to the nearest dollar.
$__________

Short Answer


35.

Find the indefinite integral.


36.

Find f( x) by solving the initial value problem.


37.

Let and compute the Riemann sum of f over
the interval , choosing the representative points to be the
midpoints of the subintervals, using: Two subintervals of equal length ( ). __________ sq units Five subintervals of equal length ( ). __________ sq units Ten subintervals of equal length ( ). __________ sq units Can you guess at the area of the region under the
graph of f on the interval ? __________sq
units


38.

The quantity demanded (in units of a hundred) of
the miniature cameras per week is related to the unit price (in dollars)
by and the quantity
(in units of a hundred) that the supplier is willing to make available in the market is related to
the unit price (in dollars) by If the market price is set at the equilibrium price, find the consumers'
surplus and the producers' surplus. Please round the answers to the nearest dollar. The
consumers' surplus: $__________ The producers' surplus: $__________

Essay


39.

Determine whether the statement is true or false. If it is true, explain why it
is true. If it is false, give an example to show why it is false. The area of the region
bounded by the graphs of and and the vertical lines
x = 0 and x = 4 is given by
