Issuu

Calculus for the Life Sciences 2nd Edition by Greenwell Ritchey and Lial ISBN 0321964039 9780321964038

Download solution manual at:

https://testbankpack.com/p/solution-manual-for-calculus-for-the-life-sciences2nd-edition-by-greenwell-ritchey-and-lial-isbn-0321964039-9780321964038/

Download full test bank at :

https://testbankpack.com/p/test-bank-for-calculus-for-the-life-sciences-2ndedition-by-greenwell-ritchey-and-lial-isbn-0321964039-9780321964038/

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem.

1) Given the velocity and initial position of a body moving along a coordinate line at time t, find the body's position at time

2) Given the velocity and initial position of a body moving along a coordinate line at time t, find the body's position at time

3) Given the velocity and initial position of a body moving along a coordinate line at time t, find the body's position at time t

4) Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, find the body's position at time t

= 9.8,

= 5, s(0) = -1

t. v = -14t + 9, s(0)

A) s = -14t2 + 9t + 12 B) s = -7t2 +

+ 12 C) s= 7t2 + 9t - 12 D) s = -7t2 + 9t - 12 1)

= 12

t v

cos π t, s(0)

1 2 A) s = 2π sin π t B) s = sin t 2 C) s = 2 sin π t + π D) s = 2 sin π t 2) π 2 π 2

v = 8 sin 4t , s(π

3) π π A) s = -2 cos 4t + 3 B) s =

cos

π π C) s =

2 cos 4t

D) s

-2 cos 4t

π π

2) = 2

4t + 4

+ 4

+ 8

B) s

1 C ) s =

v(0)

s = 9 8t2 + 5t - 1

= 4 9t2 + 5t -

5) Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, find the body's position at time t

a = 10 cos 4t, v(0) = 5, s(0) = -6

6) A certain company has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by dE = 10x + 12, where x is the number of days since the start of the job. Find dx the expenditure if the job takes 3 days. A) $4200 B) $8100 C) $42 D) $81

2 -4.9t2 - 5t - 1 D) s = 4.9t2 + 5t 4)

s = 5 cos 4t - 5t - 6 B) s = 5 sin 4t + 5t - 6 5) 8 8 C) s =5 sin 4t + 5t - 6 D) s =5 cos 4t + 5t - 6 8 8

7) After a new firm starts in business, it finds that its rate of profits (in hundreds of dollars per year)

after t years of operation is given by dP = 3t2 + 12t + 7. Find the profit in year 6 of the operation. dt

A) $16,400 B) $40,200

C) $39,200 D)

$31,000

8) In a certain memory experiment, subject A is able to memorize words at a rate given by

dm = -0.009t2 + 0.4t (words per minute). dt

In the same memory experiment, subject B is able to memorize at the rate given by

dM = -0.012t2 + 0.4t (words per minute) dt

How many more words does subject B memorize from t = 0 to t = 16 (during the first 16 minutes)?

A) 47 B) -12 C) 35 D) -4

Provide an appropriate response.

9) Which of the following integrals, if any, calculates the area of the shaded region?

5 y (-2, 4) 4 3 2 1 (2, 4) -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 A) ∫ 2 4x dx B) 4 ∫ -4x dx C) 0 ∫ -4x dx D) 0 ∫ 4x dx -2 -4 -2 -2

Find

the area of the shaded region. 10) f(x) = x3 + x26x y 10) 30 20 10 (0, 0) (3, 18) g(x) = 6x -4 -2 2 4 x -10 (-4, -24) A) 343 12 -20 -30 B) 81 12 C) 768 12 D) 937 12 11) f(x) = -x3 + x2 + 16x y 30 11) 20 10 (0, 0) (4, 16) -4 -2 2 4 6 x g(x) = 4x (-3, -12) -10 -20 -30 A) 1153 12 B) 937 12 C) 343 12 D)343 12

5 12) y = x2 - 4x + 3 12) 8 y 6 y = x - 1 4 2 -3 -2 -1 1 2 3 4 5 x -2 -4 -6 -8 A) 41 6 B) 3 C) 9 2 D) 25 6 13) y 13) 1 1 2 x y = x2 - 2x -1 -2 A) 22 15 y = -x4 B) 76 15 C) 2 D) 7 15

6 14) y = 2x2 + x - 6 y = x24 y 14) 5 4 3 2 1 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 A) 11 6 (2, 4) 1 2 3 x B) 8 3 C) 9 2 D) 19 3 15) y 6 4 2 -2 -4 2 4 6 8 10 y = x - 4 y = 2x x 15) -6 A) 64 3 B) 32 C) 32 3 D) 128 3

7 16) y = x4 - 32 y 5 16) -4 -3 -2 -1 1 2 3 4 x -5 -10 -15 -20 -25 -30 -35 -40 A) 512 5 y = -x4 B) 516 5 C) 2816 5 D) 256 5 17) 3 y 2 1 y = 2 y = 2 sin(πx) 17) 1 2 3 x -1 -2 -3 A) 4 + 4 π B) 8 C) 4 D) 4 π

8 y 18) y 2 1 y = cos2 x 18) - - 2  x 2  y = -cos x -1 -2 A) 2π 2 B) 2 + π 2 C) 2 D) 2 + π 19) y = sec2 x 19) 3 2 1 y = cos x   x 4 2 A) 12 2 B) 2 - 2 C) 2 2 D) 1 + 2 Find the area enclosed by the given curves. 20) y = 2x - x2, y = 2x - 4 20) A) 32 3 B) 31 3 C) 34 3 D) 37 3 21) y = x3, y = 4x A) 2 B) 16 C) 4 D) 8 21) 22) y = x, y = x2 A) 1 12 B) 1 3 C) 1 6 D) 1 2 22) 23) y = 1 x2, y = -x2 + 6 2

9 A) 32 B) 16 C) 8 D) 4 23)

27) Find the area of the region in the first quadrant bounded by the line y = 8x, the line x = 1, the curve y = 1 , and the x-axis x

3 4 B) 5 4 C) 6

28) Find the area of the region in the first quadrant bounded on the left by the line y = π and on the 6

28) right by the curves y = tan 2 x and y = cot 2 x. (Round to four decimal places.)

A) 0 4126 B) 4 3094 C) 0 5858 D) 0 3094 29) Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the line y = 1 x, above left by y = x + 4, and above right by y = - x2 + 10 3

A) 39 2 B) 73 6 C) 39 4 D) 15 30) Find the area between the curves y = ln x and y = ln 2x from x = 1 to x = 4. A) ln 16 B) ln 8 C) ln 2

31) Find the area of the "triangular" region in the first quadrant that is bounded above by the curve y = e3x, below by the curve y = ex, and on the right by the line x = ln 4

31) A) 4 ln 4 B) 80 3 C) 52 3 D) 18

10 24)

≤ x ≤ π A)

C) 4 D) 1 2 24) 25)

π ≤ x ≤ π 25) A) 3 -

3 2 B) 31 C) 13 D) 3 + 1 2 2 3 2 2 3 2 26) y = csc 2

= π ,

= 3π 26) 4 4 A) π B) π 2 C) π 4 D) 3π 4

y = - 4sin x, y = sin 2x, 0

16 B) 8

y = sin x, y = csc 2 x,

x, y = cot 2 x, x

and x

27)

3 2

30)

29)

D) ln 86

32) Find the area of the region between the curve y = 10x/(1 + x2) and the interval -4 ≤ x

4 of the x-axis.

33) Find the area of the region between the curve y = 72-x and the interval 0

axis

C) 10 e17 D) ln

32)

≤

A) 0

≤ x ≤ 2

33) A) 49 ln

B) 48 ln

C) 49 D) 48 ln 7

on the x-

Find the volume of the described solid.

34) The solid lies between planes perpendicular to the x-axis at x = 0 and x = 9 The cross sections perpendicular to the x-axis between these planes are squares whose bases run from the parabola y = - 3 x to the parabola y = 3 x.

A) 243 B) 729 C) 1440 D) 1458

35) The solid lies between planes perpendicular to the x-axis at x = -4 and x = 4 The cross sections perpendicular to the x-axis between these planes are squares whose bases run from the semicircle y = - 16 - x2 to the semicircle y = 16 - x2.

A) 128 3 B) 256 3 C) 512 3 D) 1024 3

36) The base of the solid is the disk x2 + y2 ≤ 25 The cross sections by planes perpendicular to the y-axis between y = - 5 and y = 5 are isosceles right triangles with one leg in the disk

A) 2000 3 B) 250 3

1250 3

1000 3

37) The solid lies between planes perpendicular to the x-axis at x = - 5 and x = 5 The cross sections perpendicular to the x-axis are semicircles whose diameters run from y = - 25x2 to y = 25 - x2

38) The solid lies between planes perpendicular to the x-axis at x = - 4 and x = 4 The cross sections perpendicular to the x-axis are circular disks whose diameters run from the parabola y = x2 to the parabola y = 32 - x2.

39) The base of a solid is the region between the curve y = 5cos x and the x-axis from x = 0 to x = π/2.

The cross sections perpendicular to the x-axis are squares with bases running from the xaxis to the curve A) 5 π B) 25 π

2 2 4

40) The base of a solid is the region between the curve y = 3cos x and the x-axis from x = 0 to x = π/2. The cross sections perpendicular to the x-axis are isosceles right triangles with one leg on the base of the solid.

9 π B) 9 π C) 3 π

34)

35)

36)

A) 125 π B) 250 π C) 1000 π D) 500 π 37)

3 3 3

A) 8192 π B) 8192 π C) 16384 π D) 256 π 38) 15 5 15 3

39)

25 π

6π

D) 2

40)

8 4 2

41) The base of a solid is the region between the curve y = 6cos x and the x-axis from x = 0 to x =

π/2

The cross sections perpendicular to the x-axis are squares with diagonals running from the xaxis to the curve

A) 9 π B) 3π C) 35 π D) 9π

2 4

41)

42) The solid lies between planes perpendicular to the x-axis at x = π/6 to x = π/2 The cross sections perpendicular to the x-axis are circular disks with diameters running from the curve y = cot x to the curve y = csc x.

43) The solid lies between planes perpendicular to the x-axis at x = -2 and x = 2 The cross sections perpendicular to the x-axis are circles whose diameters stretch from the curve y =9/ 4 + x2 to the curve y = 9/ 4 + x2

Find the volume of the solid generated by revolving the shaded region about the given axis.

42) A) (2 3 - 2) ππ2 B) ( 3 - 1) ππ2 3 2 12 C) ( 3 + 1) ππ2 D) ( 3 - 1) π + π2 2 6 6

A) 81π B) 81π2 C) 9 π2 D) 81 π2 43) 4 4

44) About the x-axis 44) 10 y 9 8 7 6 5 4 3 2 1 1 2 3 y = - 4x + 8 x A) 256 π B) 24π C) 896 π D) 128 π 3 3 3 45) About the xaxis 45) 20 y 16 12 8 4 y = 16 - x2 1 2 3 4 5 x

11 A) 128 π B) 13312 π C) 13312 π D) 8192 π 3 15 5 15

12 y y 46) About the xaxis 46) 10 y 9 8 7 6 5 4 3 2 1   4 2 y = 4sec x x A) 14π B) 16π C) 8π D) 4π 47) About the yaxis 47) 8 7 x = 7y/3 6 5 4 3 2 1 1 2 3 4 5 6 7 8 x A) 21 π B) 21π C) 98π D) 49π 2 48) About the yaxis 48) 6 5 y = 3x 4 3 2 1 1 2 3 4 5 6 x A) 3π B) 18π C) 243 π D) 27 π 5 5

13 y 49) About the yaxis 49) y 3 2  x = 2 tan y 5  2 1 2 3 x A) 5π + 5π2 B) 20π - 5π2 C) 20 - 5π D) 10π5 π2 2 50) About the yaxis 50) y 3 2 x = 2tan y 3   2 1 2 3 x A) 12π B) 6π2 + 3π C) 6π2 - 12π D) 3π2 - 6π 51) About the yaxis 51) 6 x = y2 5 5 4 3 2 1 1 2 3 4 5 6 x A) 625 π B) 25π C) 250 π D) 100π 6 3

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the xaxis.

14 y y 52) About the xaxis 52) 20 18 16 14 12 10 8 6 4 2 1 2 3 4 y = 4 - x2 x A) 224 π B) 256 π C) 64 π D) 8 π 15 15 15 3 53) About the xaxis 53) 4 y = 2 sin x 2  x 2 A) 2π2 - 4π B) 2π2 + 4π C) 2π2 D) 2π2 - 2π

54) y = x, y = 0, x

3, x

5 A) 2 π B) 98 π C) 17π D) 8π 54) 3 3 55) y = x, y = 0, x = 0, x = 7 A) 7 π B) 7π C) 49 π D) 49 π 55) 2 2 3 56) y = x2, y = 0, x = 0, x = 6 A) 1944π B) 324π C) 72π D) 7776 π 5 56)

15 57) y = 2x + 3, y = 0, x = 0, x = 1 57) A) 3π 2 B) 2π C) 4π D) π

16 58) y = 1 , y = 0, x = 1, x = 9 x A) πln 9 B) 8 π C) 1 π D) 4 π 58) 9 3 9 59) y = x + 1, y = 0, x = -1, x = 4 A) 12π B) 5 π C) 125 π D) 25π 59) 2 3 60) y = 64 - x2, y = 0, x = 0, x = 8 A) 2048 π B) 1024 π C) 256π D) 16π 60) 3 3 61) y = sin 7x, y = 0, 0 ≤ x ≤ π 7 A) 14π B) 2π C) 7π D) 2 π 7 61) 62) y = 3csc x, y = 0, x = π , x = 3π 62) 4 4 A) 9π B) 18π C) 6π D) 27π 63) y = 7cos πx, y = 0, x = -0 5, x = 0 5 A) 49π B) 98π C) 49 π D) 49 π 63) 2 3 64) y = 1 , y = 0, x = 1, x = 9 x A) 3π B) π 9 C) π (ln 9) D) π(ln 9) 2 64) 65) y = 2x, y = 2, x = 0 A) 1π B) 6π C) 4 π D) 8 π 65) 3 3 66) y = - 6x + 12, y = 6x, x = 0 A) 36π B) 216π C) 72π D) 12π 66) 67) y = 7x, y = 7, x = 0

17 A) 98π B) 343 π C) 343 π D) 343 π 67) 3 2 4 68) y = x2 , y = 9, x = 0 A) 243 π B) 972 π C) 18π D) 1458 π 68) 5 5 5

Find the volume of the solid generated by revolving the region about the y-axis.

18 69) y = x2 + 4, y = 3x + 4 A) 342 π B) 144 π C) 27π D) 603 π 69) 5 5 5 70) y = 4 , y = - x + 5 x A) 12π B) 27 π C) 125 π D) 9π 70) 4 3 71) y = sin 5x, y = 1, x = 0 to x = π 10 A) π2 + π B) π2 - π C) π1 D) π2π 71) 10 10 10 5 10 5 72) y = 6csc x, y = 6 2, π ≤ x ≤ 3π 72) 4 4 A) π2 + 12π B) 36π2 - 72π C) 6π2 - 36π D) 36π2 + 72π 73) y = 7cos (πx), y = 7, x = -0.5, x = 0.5 A) 98π B) 49 π C) 49π D) 49 π 73) 3 2 74) y = sec x, y = tan x, x = 0, x = π 4 74) A) π 4 B) π 2 C) π2 4 D) π2 2

75) The region enclosed by x = y2

x = 0, y

2, y

2 2 A) 64 π B) 8 π C) 8 π D) 16 π 75) 5 3 5 5 76) The region enclosed by x = y1/3, x = 0, y = 64 A) 256π B) 1024π C) 192π D) 3072 π 5 76) 7

= -

19 ) The region enclosed by x = 3 , x = 0, y = 1, y = 5 y A) 36 π B) 36 π C) 54 π D) 12 π 77) 5 25 5 5

78) The region enclosed by x = 2tan y

79) The region enclosed by x = sin 5y, 0 ≤ y ≤

, x =

80) The region enclosed by the triangle with vertices (4, 0), (4, 2), (6, 2)

81) The region enclosed by the triangle with vertices (0, 0), (5, 0), (5, 2)

82) The region in the first quadrant bounded on the left by the circle x2 + y2 = 25, on the right by the line x = 5, and above by the line y = 5

83) The region in the first quadrant bounded on the left by y = x3, on the right by the line x = 2, and below by the x-axis

84) The region in the first quadrant bounded on the left by y = 4 , on the right by the line x = 4, and x

above by the line y = 2 A) 16π B) 16 π C) 24π

Find the volume of the solid generated by revolving the region about the given line.

85) The region bounded above by the line y = 16, below by the curve y = 16 - x2, and on the right by the line x = 4, about the line y = 16 A) 64 π B) 7168 π C) 1024 π D) 8192 π

3 15 5 15

86) The region in the second quadrant bounded above by the curve y = 4 - x2, below by the xaxis, and on the right by the y-axis, about the line x = 1

A) 256 π B) 8π C) 32 π D) 56 π

x = 0, y =5π 78) 5 4 A) 5π + 5π2 B) 20 - 5π C) 10π5 π2 D) 20π - 5π2 2

0 10 A) 10π B) π 5 C) π 10 D) 5π 79)

A) 40 π B) 152 π C) 28 π D) 56 π 80) 3 3 3 3

A) 100 π B)

π C) 100π D) 25 π 81) 3 3 3

A) 125π B) 250 π C) 125 π D) 125 π 82) 3 4 3

A) 64 π B)

π C) 96 π D) 4π 83) 5 5 5

84)

D) 8π

85)

86)

15 3

Solve the problem.

87) The disk (x - 6)2 + y2 ≤ 1 is revolved about the y-axis to generate a torus. Find its volume. (Hint: 1

- y2 dy -1 = 1 π, since it is the area of a semicircle of radius 1 ) 2

88) The hemispherical bowl of radius 5 contains water to a depth 4

89) A water tank is formed by revolving the curve y = 2x4 about the y-axis. Find the volume of water in the tank as a function of the water depth, y.

90) A water tank is formed by revolving the curve y = 7x4 about the y-axis Water drains from the tank through a small hole in the bottom of the tank At what constant rate does the water level, y, fall? (Use Torricelli's Law: dV/dt = -m y.)

91) A right circular cylinder is obtained by revolving the region enclosed by the line x = r, the xaxis, and the line y = h, about the y-axis Find the volume of the cylinder.

92) A frustum of a right circular cone has a height of 10 m, a base of radius 2m, and a top of radius 1m. Find its volume.

93) An auxiliary fuel tank for a helicopter is shaped like the surface generated by revolving the curve

y = 1x2 , - 4

x ≤ 4, about the x-axis (dimensions are in feet) How many cubic feet of fuel will 16

87) ∫ 1

A) 3π2 B) 12π2 C) 6π2 D) 6π

volume of

bowl A) 88 π B) 301 π C) 142π D) 176 π 88) 3 3 3

Find the

water

the

89) A) V(y) = 2π 3 2 y3/2 B) V(y) = π 2 2 y1/2 C) V(y) = π y9 D) V(y) = 3π y3/2 9 2 2

90) A) dy = - π B) dy = - 7 C) dy = - m π D) dy = - m 7 dt m 7 dt m π dt 7 dt π

A) πr2h B) πrh C) πrh2 D) 2πr2h 91)

A) 7π B) 70 π C) 70π D) 7 π 92) 3 3

t h e ta n

≤

k hold to the nearest cubic foot?

A) 7 B) 4

13 D) 17

94) An auxiliary fuel tank for a helicopter is shaped like the surface generated by revolving the curve

y = 1x2 , - 2 ≤ x ≤ 2, about the x-axis (dimensions are in feet). If a cubic foot holds 7.481 gallons 4 and the helicopter gets 3 miles to the gallon, how many additional miles will the helicopter be able to fly once the tank is installed (to the nearest mile)?

A) 75 B) 50 C) 150 D) 38

93)

94)

95) Find the volume that remains after a hole of radius 1 is bored through the center of a solid sphere of radius 4.

96) Find the volume that remains after a hole of radius 1 is bored through the center of a solid cylinder of radius 2 and height 4.

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis.

23 y y

A) 27π B) 160 π C) 54π D) 256 π 95) 3 3

A) 16π B) 6π C) 12π D) 4π 96)

97) About the xaxis 97) 6 5 4 x = y2/3 3 2 1 1 2 3 4 5 6 x A) 9π B) 18π C) 27 π D) 27 π 2 4 98) About the yaxis 98) x = 3 6 5 4 y = 3x 3 2 1 1 2 3 4 5 6 x A) 27 π B) 108 π C) 54 π D) 12π 5 5 5

24 y y y 99) About the x-axis y = 5 x = 5 5 4 3 2 1 99) x = 25 - y2 1 2 3 4 5 x A) 125 π B) 250 π C) 125 π D) 125π 3 3 6 100) About the yaxis 100) x = 4 4 3 y = 2 + x2/16 2 1 1 2 3 4 5 x A) 48π B) 32π C) 40π D) 20π 101) About the y-axis x = 3 101) 4 3 y = 3 - x2/9 2 1 1 2 3 4 5 x A) 18π B) 45 π C) 27π D) 45 π 4 2

20 y y 102) About the y-axis x = 5 102) 4 y = x2 + 4 3 2 1 1 2 3 x A) 19π B) 38 π C) 18π D) 19 π 3 3 103) About the yaxis 103) 7 6 5 4 3 y = 4x - x2 2 1 1 2 3 4 5 x A) 64 π B) 128 π C) 32π D) 64π 3 3 104) About the xaxis 104) y 4 3 y = 9 - x2 1 1 2 3 4 5x A) 27π B) 81 π C) 18π D) 9π 2

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis.

21 y (0, 4) y 105) About the yaxis 105) 4 3 2 y =3sin(x2) 1 1.8 x A) 9π B) 12π C) 6π D) 3π 106) About the yaxis 106) y = 4sin (x) ; 0 < x ≤ π x  x A) 12π B) 8π C) 20π D) 16π

107) y = 9x, y =x , x = 1 9 A) 163 π B) 164 π C) 82π D) 82 π 107) 27 27 27 108) y = 4x, y = 8x, x = 4 A) 256 π B) 128 π C) 512 π D) 384π 108) 3 3 3 109) y = 5x2, y = 5 x A) 3π B) 3 π C) 15 π D) 3 π 109) 4 4 2 110) y = x2, y = 4 + 3x, for x ≥ 0

22 A) 96π B) 192π C) 64π D) 32π 110)

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis.

= 1

23 111) y = 32 - x2, y = x2, x = 0 A) 512π B) 128π C) 64π D) 256π 111) 112) y = 3x3, y = 3x, for x ≥ 0 A) 1 π B) 4 π C) 2 π D) 6 π 112) 5 5 5 5 113) y = 3 , y = 0, x = 1, x = 9 x A) 108π B) 104π C) 52π D) 112π 113) 114) y = 5 x, y = 0, x = 1 A) 2π B) 4π C) 25π D) 10π 114) 115) y = 4 , y = 0, x = 3, x = 5 x A) 24π B) 12π C) 16π D) 8π 115) 116) y = x2 - 3, y = 2x, x = 0, for x ≥ 0 A) 45π B) 18π C) 45 π D) 45 π 116) 4 2 117) y = 6e-x2 , y = 0, x = 0, x = 1 117) A) 12 11 e π B) 6(e - 1) π C) 6 11 e π D) 12 1 + 1 π e 118) y = 3ex2, y = 0, x = 0, x = 1 A) 6(e - 1) π B) 6e π C) 3(e - 1) π D) 3 (e - 1) π 2 118)

119) x = 6 y, x

- 6y, y

A) 22 π B) 44 π C) 12π D) 16π 119) 5 5

24 120) x = 3y2, x = - 3y, y = 3 A) 351 π B) 351 π C) 351π D) 351 π 120) 8 4 2 121) x = 6y - y2, x = 0 A) 108π B) 432π C) 36π D) 216π 121) 122) y = 6 x , y = 6 A) 1728π B) 24π C) 48π D) 2π 122)

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines.

x = 2; revolve about the x-

25 123) y = 7x, y = 14x, y = 7 A) 49 π B) 49 π C) 49 π D) 49π 123) 6 3 2 124) y = x, y = 0, y = x - 6 A) 27π B) 63 π C) 225 π D) 63 π 124) 2 2 4 125) y = 4x2, y = 4 x A) 12 π B) 24π C) 6 π D) 24 π 125) 5 5 5 126) x = 8 - y2, x = y2, y = 0 A) 32π B) 8π C) 16π D) 4π 126) 127) x = 8y2 , x = 8 3 y A) 12π B) 8 π C) 10 π D) 20 π 127) 3 7 7 128) y = 5x3, y = 5x, for x ≥ 0 A) 100 π B) 50 π C) 4 π D) 100 π 128) 3 21 3 21 129) x = 1 ey2, y = 0, x = 0, y = 1 7 A) 7 πe B) π (e - 1) C) π(e - 1) D) 7π(e1) 129) 2 7 130) x = 3e- y2, y = 0, x = 0, y = 1 130) A) 3 11 e π B) 6 11 e π C) 3(e - 1) π D) 6 1 + 1 π e

131) y = 4x, y = 0,

axis 131)

26 A) 64 B) 128 π C) 256 π D) 64 π 3 3 3 3 132) y = 2x, y = x2; revolve about the y-axis A) 8 π B) 4 π C) 56 π D)8 π 132) 3 3 3 3 133) y = 9 - x2, y = 9, x = 3; revolve about the line y = 9 A) 243 π B) 9π C) 567 π D) 648 π 133) 5 5 5

y = 5x, y = 0, x = 3; revolve about the line x

Find the volume of the solid generated by revolving the region about the given axis. Use the shell or washer method.

The triangle with vertices (0, 0), (0, 2), and (1, 2) about the line x = 1

The region bounded by x = 6 y, x = - 6y, and y = 1 about the line y = 1

The region bounded by y = 8 x, y = 8, and x = 0 about the line y = 8

The region bounded by y = 3 x, y = 3, and x = 0 about the line x = 1

The region bounded by y = 8 x, y = 8, and x = 0 about the y-axis

The region bounded by y = 5x - x2 and y = x about the y-axis

The region bounded by y = 7x - x2 and y = x about the line x = 6

The region in the first quadrant bounded by x = 2y - y2 and the y-axis about the yaxis

27 134)

-1 134) A) 135 2 B)

π C) 135 π D) 45π 2

135

A) 4 π B) 2 π C) 5 π D) 1 π 135) 3 3 3 3 136)

A) 6π B)

π D) 44 π 136) 5 5 5 137)

A) 32π B) 32 π C) 16 π D) 64 π 137) 3 3 3 138)

A) 7 π B) 17 π C) 7 π D) 8 π 138) 5 5 10 5 139)

A) 4 π B)

π C)

π D) 8 π 139) 5 3 3 5 140)

A) 64π B)

π C) 64 π D) 128 π 140) 3 3 141)

A) 216π B)

π D) 324π 141) 142)

A) 4 π B) 32 π C) 16 π D) 16 π 142)

135)

C) 22

108π

162

143) The region in the first quadrant bounded by x = 4y - y2 and the y-axis about the xaxis

144) The region in the first quadrant bounded by x = 2y - y2 and the y-axis about the line x = -1

28 5 15 15 5

A) 64π B) 64 π C) 32π D) 128 π 143) 3 3

A) 14 π B) 56 π C) 56 π D) 112 π 144) 5 15 5 15

Solve the problem.

145) A bead is formed from a sphere of radius 2 by drilling through a diameter of the sphere with a drill bit of radius 1 Find the volume of the bead

146) A water noodle is formed from a cylinder of radius 4 and height 8 by drilling through the diameter of the cylinder with a drill bit of radius 1 Find the volume of the water noodle

147) An auxiliary fuel tank for a helicopter is shaped like the surface generated by revolving the curve

y = 1x2 , - 3 ≤ x ≤ 3, about the x-axis (dimensions are in feet) How many cubic feet of fuel will 9 the tank hold to the nearest cubic foot?

A) 5 π B)

π C) 8 π D) 10 π 145) 3 3 3 3

A) 128π B) 8π C) 120π D) 60π 146)

A) 5 B) 3 C) 13 D) 10 147)

the length of the curve. 148) y = 4x3/2 from x = 0 to x = 5 16 148) A) 335 3 B) 335 432 C) 335 288 D) 9 16 149) y = (4 - x2/3) 3/2 from x = 1 to x = 8 A) 6 B) 9 C) 18 D) 12 149) 150) y = 1 x3 + 1 from x = 1 to x = 4 150) 6 2x A) 261 32 B) 11 C) 87 4 D) 87 8 151) y = 3 (x4/3 - 2x2/3) from x = 1 to x = 8 8 A) 23 B) 17 2 C) 81 8 D) 63 8 151) 152) x = y4 + 1 from y = 1 to y = 2 152) 8 4y2 A) 2 B) 17 8 C) 33

Find

30 16 D) 33 8 153) x = 2 (y - 1) 3/2 from y = 16 to y = 25 3 153) A) 122 3 B) 4 C) 61 D) 183 2 E) 109 3

31 154) x = 1 y 3/2 - y 1/2 from x = 1 to x = 4 3 154) A) 7 3 B) 10 3 C) 2 D) 5 x 155) y = ∫ 1 t2 - 1 dt , 2 ≤ x ≤ 5 155) A) 6 B) 14 C) 21 2 D) 21 1 156) x = ∫ y t3 - 1 dt , 1 ≤ y ≤ 9 156) A) 20 B) 481 5 C) 484 5 D) 52 3 x 157) y = ∫ 0 16 sin2t - 1 dt , 0 ≤ x ≤ π 2 157) A) 16 B) 2 C) 4 3 D) 4 Set up an integral for the length of the curve. 158) y = x6, 0 ≤ x ≤ 1 1 1 158) A) ∫ 0 1 1 + 6x10 dx B) ∫ 0 1 1 + 6x5 dx C) ∫ 0 1 + 36x12 dx D) ∫ 0 1 + 36x10 dx 159) y = 1 - x3,1 ≤ x ≤ 1 159) 4 4 A) ∫ 1/4 4 - 4x3 + 3x2 dx B) ∫ 1/4 4 - 4x3 + 9x4 dx -1/4 1/4 C) ∫ -1/4 4(1 - x3) 4 + 9x4 dx 4 -1/4 1/4 D) ∫ -1/4 4(1 - x3) 5 - 4x3 dx 4(1 - x3) 160) x = y1/7, 0 ≤ y ≤ 2 160)

32 2 A) ∫ 0 2 C) ∫ 0 49y12/7 + 1 dy 49y12/7 7y6/7 + 1 dy 7y6/7 2 B) ∫ 0 2 D) ∫ 0 2 dy 49y12/7 1 dy 49y12/7

33 161) x = y2 + 2y, 0 ≤ y ≤ 2 2 2 161) A) ∫ 0 2 4y2 + 5 dy B) ∫ 0 2 4y2 + 4y + 4 dy C) ∫ 0 4y2 + 8y + 5 dy D) ∫ 0 2y + 3 dy 162) y = 7 cot x, π ≤ x ≤ π 162) A) ∫ 4 π/2 2 1 + 49 csc4 x dx B) ∫ π/2 1 + 7 csc2 x dx π/4 π/2 C) ∫ π/4 1 - 49 csc2 x dx π/4 π/2 D) ∫ π/4 1 + 49 csc2 x dx 163) y = 6 cos x, 0 ≤ x ≤ π π π 163) A) ∫ 0 π 1 + 36 sin2 x dx B) ∫ 0 π 1 + 36 cos2 x dx C) ∫ 0 1 + 6 sin x dx D) ∫ 0 1 - 6 sin x dx 164) x = sin 5y, - π ≤ y ≤ 0 0 0 164) A) ∫ -π 0 1 + 5 cos 5y dy B) ∫ -π 0 1 + 25 cos2 5y dy C) ∫ -π 1 + cos2 5y dy D) ∫ -π 1 + 25 sin2 5y dy 165) x = 6 tan y, 0 ≤ y ≤ π 4 π/4 π/4 165) A) ∫ 0 π/4 1 - 36 sec2 y dy B) ∫ 0 π/4 1 + 36 sec4 y dy C) ∫ 0 1 + 36 sec2 y dy D) ∫ 0 1 + 6 sec4 y dy

34 166) y4 + 4y = 4x - 1, 1 ≤ y ≤ 2 2 2 166)

∫ 1 2 y3 + 2 dy

∫ 1 2 y6 + y3 + 1 dy

∫ 1 y6 + 2 dy

∫ 1 y6 + 2y3 + 2 dy

35 x 167) y = ∫ cot t dt , π ≤ x ≤ π 167) 6 3 0 π/3 π/3 A) ∫ π/6 π/3 1 + cot x dx B) ∫ π/6 π/3 csc x dx C) ∫ π/6 csc x dx D) ∫ π/6 1 + csc4 x dx Solve the problem. 168) Find a curve through the point 1, 5 6 2 whose length integral, 1 ≤ x ≤ 2, is L = ∫ 1 1 + 25x10 dx. 168) A) y = 5x6 B) y = 5 x6 C) y = 5x5 D) y = 5 x5 6 6 2 169) Find a curve through the point (-6, 1) whose length integral, 1 ≤ y ≤ 2, is L = ∫ 1 1 + 9 dy y3 169) A) x = -6 y B) x = -6y5/2 C) x = -6 y D) x = 3 y 1 170) Find a curve through the point (0, 5) whose length integral, 0 ≤ x ≤ 1, is L = ∫ 0 1 + 4x2 dx. 170) A) y = x2 + 5 B) y = x C) y = x2 D) y = 2x + 5 Find the area of the surface generated when the given curve is revolved about the xaxis. 171) y = 6x + 5 on [0, 6] 171) A) 276 37π B) 276π 37 C) 264 37π D) 276π 172) y = x on 3 , 9 172) 2 2 A) 7 7π 6 C) 7 7π 2 B) π (19 19 - 7 7) 6 D) π (21 7 - 3) 6 173) y = x3 9 on 0, 2 173) A) 256 π B) 98π C) 98 π D) 1163 π

36 27 81 2187