Deck 7: Section 4: Applications of Integration

Question 1

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

A)
B)
C)
D)
E)

Answer 1

Question 2

Find the arc length of the graph of the function over the interval .

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the arc length of the graph of the function over the interval [14, 16].

A)
B)
C)
D)
E)

Answer 3

Question 4

An ornamental light bulb is designed by revolving the graph of about the x-axis where x and y are measured in feet. Approximate the amount of glass needed to make the bulb. (Assume that the glass is 0.016 inches thick.) Round your answer to four decimal places.

A)
B)
C)
D)
E)

Question 5

Electrical wires suspended between two towers form a catenary modeled by the equation where x and y are measured in meters. The towers are 50 meters apart. Find the length of the suspended cable. Round your answer to three decimal places.

A) 94.421m
B) 50.000 m
C) 64.077 m
D) 40.048 m
E) 47.211 m

Question 6

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

A)
B)
C)
D)
E)

Question 7

A bridge has a main span of about 1400 meters. Each of its towers has a height of about 146 meters. Approximate the length of a parabolic cable along the main span if the length C of the cable is given by . Round your answer to one decimal place.

A) 719.8 meters
B) 759.4 meters
C) 2120.7 meters
D) 1439.6 meters
E) 2879.2 meters

Question 8

Find the arc length of the graph of the function over the interval [1,64].

A)
B)
C)
D)
E)

Question 9

Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of about the x-axis.

A)
B)
C)
D)
E)

Question 10

A barn is 75 feet long and 50 feet wide. A cross section of the roof is the inverted catenary . Find the number of square feet of roofing on the barn. Round your answer to the nearest integer.

A) 4180 square feet
B) 4200 square feet
C) 2100 square feet
D) 1875 square feet
E) 3750 square feet

Question 11

Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of about the y-axis. Round your answer to three decimal places.

A) 58.659
B) 117.319
C) 235.685
D) 5.323
E) 2.661

Question 12

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

A)
B)
C)
D)
E)

Question 13

Use the integration capabilities of a graphing utility to approximate the arc length of the graph of on the interval . Round your answer to three decimal places.

A) 3.620
B) 5.020
C) 10.540
D) 3.820
E) 5.270

Question 14

Find the arc length of the graph of the function over the interval [1,2].

A)
B)
C)
D)
E)

Question 15

Find the arc length of the graph of the function over the interval .

A)
B)
C)
D)
E)

Question 16

Find the arc length of the graph of the function over the interval [0,6].

A)
B)
C)
D)
E)

Question 17

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

A)
B)
C)
D)
E)

Question 18

Find the arc length from clockwise to (2, ) along the circle . Round your answer to four decimal places.

A) 4.1888
B) 0.2618
C) 0.1309
D) 1.8546
E) 2.0944