Deck 5: Integrals

Question 1

Sketch the region bounded by the graphs of the given equations and find the area of that region.

Answer 1

Question 2

Answer 2

Question 3

Use a computer algebra system to find the exact volume of the solid obtained by rotating the region
bounded by the given curves about the specified line.

Answer 3

Question 4

Question 5

Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region
bounded by the given curves about the specified axis.

Question 6

Sketch the region bounded by the graphs of the given equations and find the area of that region.

Question 7

Find the area of the region bounded by the curves.

Question 8

Racing cars driven by Chris and Kelly are side by side at the start of a race.The table shows the
velocities of each car (in miles per hour) during the first ten seconds of the race.Use the Midpoint
Rule to estimate how much farther Kelly travels than Chris does during the first ten seconds.

Question 9

Question 10

Question 11

Find the average value of the function on the given interval.

Question 12

Find the area of the region bounded by the given curves (a) using integration with respect to x and
(b) using integration with respect to y.

Question 13

Use the method of disks or washers, or the method of cylindrical shells to find the volume of the
solid generated by revolving the region bounded by the graphs of the equations about the indicated
axis.Sketch the region and a representative rectangle.

Question 14

Find the area of the region bounded by the curves.

Question 15

Find the volume of the solid generated by revolving the region bounded by the graphs of the
equations about the indicated axis.

Question 16

Sketch the region bounded by the graphs of the given equations and find the area of that region.

Question 17

Question 18

Find the volume of the solid generated by revolving the region bounded by the graphs of the
equations about the indicated line.Sketch the region and a representative rectangle.

Question 19

Use a graphing utility to (a) plot the graphs of the given functions and (b) find the x-coordinates of
the points of intersection of the curves.Then find an approximation of the area of the region
bounded by the curves using the integration capabilities of the graphing utility.Round answers to
two decimal places.

Question 20

Question 21

Find the volume of the solid generated by revolving the region bounded by the graphs of the
equations about the indicated line.Sketch the region and a representative rectangle.

Question 22

Use the method of cylindrical shells to find the volume of the solid generated by revolving the
region bounded by the graphs of the equations about the indicated axis.Sketch the region and a
representative rectangle.

Question 23

Find the volume of the solid generated by revolving the region bounded by the graphs of the
equations about the indicated axis.

Question 24

Sketch the region bounded by the graphs of the given equations and find the area of that region.

Question 25

Question 26

Use the method of cylindrical shells to find the volume of the solid generated by revolving the
region bounded by the graphs of the equations about the indicated axis.Sketch the region and a
representative rectangle.

Question 27

Question 28

Find the volume of the solid generated by revolving the region bounded by the graphs of the
equations about the indicated axis.

Question 29

Use a graphing utility to (a) plot the graphs of the given functions and (b) find the approximate
x-coordinates of the points of intersection of the graphs.Then find an approximation of the volume
of the solid obtained by revolving the region bounded by the graphs of the functions about the x-axis.
Round answers to two decimal places.

Question 30

Question 31

Question 32

Question 33

Question 34

Question 35

A chain weighing 4 lb/ft hangs vertically from a winch located 11 ft above the ground, and the free
end of the chain is just touching the ground.Find the work done by the winch in pulling in the
whole chain.

Question 36

Use the method of cylindrical shells to find the volume of solid obtained by rotating the region
bounded by the given curves about the x-axis.

Question 37

Question 38

Question 39

Sketch the region bounded by the graphs of the given equations and find the area of that region.

Question 40

Find the area of the region bounded by the given curves (a) using integration with respect to x and
(b) using integration with respect to y.

Question 41

Sketch the region bounded by the graphs of the given equations and find the area of that region.

Question 42

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line.

Question 43

Use the method of cylindrical shells to find the volume of solid obtained by rotating the region bounded by the given curves about the specified axis.

Question 44

Question 45

Use the method of disks or washers, or the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated
Axis.Sketch the region and a representative rectangle.

Question 46

Question 47

Question 48

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line.Sketch the region and a representative rectangle.

Question 49

Question 50

Question 51

Question 52

Use cylindrical shells to find the volume of the solid.

Question 53

Question 54

The base of a solid is a circular disk with radius .Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the
Base.

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60