Name: __________________________ Date: _____________



1.
Find the area of the region bounded by the equations by integrating (i) with respect to x and (ii) with respect to y.

A.
B.
C.
D.
E.


2.
Find the area of the region bounded by the graphs of the algebraic functions.

A.
B.
C.
D.
E.


3.
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the y-axis.

A.
B.
C.
D.
E.


4.
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines.



(i) x-axis; (ii) the line y = 102
A.
(i) ;
B.
(i) ;
C.
(i) ;
D.
(i) ;
E.
(i) ;


5.
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. Verify your results using the integration capabilities of a graphing utility.

A.
B.
C.
D.
E.


6.
Use the shell method to set up and evaluate an integral that gives the volume of the solid generated by revolving the plane region about the y-axis.

A.
B.
C.
D.
E.


7.
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.

A.
B.
C.
D.
E.


8.
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 10.

A.
B.
C.
D.
E.


9.
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines.



(i) x-axis; (ii) the line y = 13
A.
(i) ;
B.
(i) ;
C.
(i) ;
D.
(i) ;
E.
(i) ;


10.
Find the arc length of the graph of the function over the interval [1,1000].
A.
B.
C.
D.
E.


11.
Find the area of the surface generated by revolving the curve about the y-axis.

A.
B.
C.
D.
E.


12.
Find the area of the surface generated by revolving the curve about the y-axis.

A.
B.
C.
D.
E.


13.
Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.

A.
280.8 lb
B.
3,120 lb
C.
624 lb
D.
2,496 lb
E.
31.2 lb


14.
The figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot. Dimensions in the figure are in feet. Determine force on this part of the concrete form.

A.
140.7 lb
B.
10,130.4 lb
C.
1,688.4 lb
D.
703.5 lb
E.
6,753.6 lb


15.
A cylindrical gasoline tank is placed so that the axis of the cylinder is horizontal. Find the fluid force on a circular end of the tank if the tank is half full, assuming that the diameter is 4 feet and the gasoline weighs 42 pounds per cubic foot.
A.
224 lb
B.
112 lb
C.
448 lb
D.
896 lb
E.
1,792 lb



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