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Let R be the region bounded by the given curves. Find the volume of the solid generated when R is revolved about the given line. -x = 0, y = Let R be the region bounded by the given curves. Find the volume of the solid generated when R is revolved about the given line. -x = 0, y = , and y = 2; about y = 2 A) 8 \pi /3 B) 9 \pi /4 C) 11 \pi /4 D) 10 \pi /3 , and y = 2; about y = 2


A) 8 π\pi /3
B) 9 π\pi /4
C) 11 π\pi /4
D) 10 π\pi /3

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Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = , y = 0, x = 0, x = 9 A) 9 \pi B) 81/2 \pi C) 27 \pi D) 9/2 \pi -y = Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = , y = 0, x = 0, x = 9 A) 9 \pi B) 81/2 \pi C) 27 \pi D) 9/2 \pi , y = 0, x = 0, x = 9


A) 9 π\pi
B) 81/2 π\pi
C) 27 π\pi
D) 9/2 π\pi

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Solve the problem. -A diving pool that is 5 m deep and full of water has a viewing window on one of its vertical walls. Find the force on a square window, 2 m on a side, with the lower edge of the window on the bottom of the pool.


A) 49,000 N
B) 39,200 N
C) 156,800 N
D) 25,600 N

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Find the area enclosed by the given curves. -y = Find the area enclosed by the given curves. -y = x<sup>2</sup>, y = -x<sup>2</sup> + 6 A) 8 B) 16 C) 32 D) 4 x2, y = -x2 + 6


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

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Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = , y = 0, x = 1, x = 5 A) 2/5 \pi B) \pi ln 5 C) 3/5 \pi D) 4/5 \pi -y = Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = , y = 0, x = 1, x = 5 A) 2/5 \pi B) \pi ln 5 C) 3/5 \pi D) 4/5 \pi , y = 0, x = 1, x = 5


A) 2/5 π\pi
B) π\pi ln 5
C) 3/5 π\pi
D) 4/5 π\pi

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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. -x = 6 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. -x = 6 , y = 0, x = 0, y = 1 A) 6 \pi B) 12 \pi C) 6(e - 1) \pi D) 12 \pi , y = 0, x = 0, y = 1


A) 6 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. -x = 6 , y = 0, x = 0, y = 1 A) 6 \pi B) 12 \pi C) 6(e - 1) \pi D) 12 \pi π\pi
B) 12 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. -x = 6 , y = 0, x = 0, y = 1 A) 6 \pi B) 12 \pi C) 6(e - 1) \pi D) 12 \pi π\pi
C) 6(e - 1) π\pi
D) 12 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. -x = 6 , y = 0, x = 0, y = 1 A) 6 \pi B) 12 \pi C) 6(e - 1) \pi D) 12 \pi π\pi

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Find the area of the shaded region. -Find the area of the shaded region. - A) 9/2 B) 8/3 C) 19/3 D) 11/6


A) 9/2
B) 8/3
C) 19/3
D) 11/6

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Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the y-axis Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the y-axis A) 12 \pi B) 5 \pi C) 8 \pi D) 10 \pi


A) 12 π\pi
B) 5 π\pi
C) 8 π\pi
D) 10 π\pi

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Solve the problem. -An auxiliary fuel tank for a helicopter is shaped like the surface generated by revolving the curve Solve the problem. -An auxiliary fuel tank for a helicopter is shaped like the surface generated by revolving the curve - 4 \le x \le 4, about the x-axis (dimensions are in feet) . If a cubic foot holds 7.481 gallons 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) 301 B) 75 C) 100 D) 150 - 4 ≤\le x ≤\le 4, about the x-axis (dimensions are in feet) . If a cubic foot holds 7.481 gallons 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) 301
B) 75
C) 100
D) 150

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Solve the problem. -Hooke's law is applicable to idealized (linear) springs that are not stretched or compressed too far. Consider a nonlinear spring whose restoring force is given by F(x) = 18x - 0.3 Solve the problem. -Hooke's law is applicable to idealized (linear) springs that are not stretched or compressed too far. Consider a nonlinear spring whose restoring force is given by F(x) = 18x - 0.3 , for |x| \le 9. How much work is done in stretching the spring from its equilibrium position (x = 0) to x = 1? Round to two decimal places when appropriate. A) 473.85 J B) 8.93 J C) 236.93 J D) 17.7 J , for |x| ≤\le 9. How much work is done in stretching the spring from its equilibrium position (x = 0) to x = 1? Round to two decimal places when appropriate.


A) 473.85 J
B) 8.93 J
C) 236.93 J
D) 17.7 J

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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. -x = 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. -x = , y = 0, x = 0, y = 1 A) 4 \pi (e - 1) B) \pi (e - 1) C) 2 \pi e D) (e - 1) 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. -x = , y = 0, x = 0, y = 1 A) 4 \pi (e - 1) B) \pi (e - 1) C) 2 \pi e D) (e - 1) , y = 0, x = 0, y = 1


A) 4 π\pi (e - 1)
B) π\pi (e - 1)
C) 2 π\pi e
D) 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. -x = , y = 0, x = 0, y = 1 A) 4 \pi (e - 1) B) \pi (e - 1) C) 2 \pi e D) (e - 1) (e - 1)

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Find the area enclosed by the given curves. -Find the area of the region in the first quadrant bounded by the line y = 8x, the line x = 1, the curve Find the area enclosed by the given curves. -Find the area of the region in the first quadrant bounded by the line y = 8x, the line x = 1, the curve and the x-axis. A) 3/4 B) 3/2 C) 6 D) 5/4 and the x-axis.


A) 3/4
B) 3/2
C) 6
D) 5/4

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Solve the problem. -A frustum of a right circular cone has a height of 10 m, a base of radius 6m, and a top of radius 5m. Find its volume.


A) 91 π\pi
B) 910 /3 π\pi
C) 91/3 π\pi
D) 910 π\pi

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Find the area of the shaded region. - Find the area of the shaded region. - A) 2 B) 2 + \pi C) 2 - D) 2 +


A) 2
B) 2 + π\pi
C) 2 - Find the area of the shaded region. - A) 2 B) 2 + \pi C) 2 - D) 2 +
D) 2 + Find the area of the shaded region. - A) 2 B) 2 + \pi C) 2 - D) 2 +

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Find the length of the curve. -x = Find the length of the curve. -x = + from y = 1 to y = 2 A) 33/16 B) 2 C) 33/8 D) 17/8 + Find the length of the curve. -x = + from y = 1 to y = 2 A) 33/16 B) 2 C) 33/8 D) 17/8 from y = 1 to y = 2


A) 33/16
B) 2
C) 33/8
D) 17/8

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Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = , y = 0, x = 0, x = 1 A) 4 \pi B) 3 \pi /2 C) \pi D) 2 \pi -y = Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = , y = 0, x = 0, x = 1 A) 4 \pi B) 3 \pi /2 C) \pi D) 2 \pi , y = 0, x = 0, x = 1


A) 4 π\pi
B) 3 π\pi /2
C) π\pi
D) 2 π\pi

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Find the volume of the solid generated by revolving the region about the y-axis. -The region in the first quadrant bounded on the left by y = Find the volume of the solid generated by revolving the region about the y-axis. -The region in the first quadrant bounded on the left by y = , on the right by the line , and above by the line y = 2 A) 25 \pi B) 25/3 \pi C) 25 /2 \pi D) 75 /2 \pi , on the right by the line Find the volume of the solid generated by revolving the region about the y-axis. -The region in the first quadrant bounded on the left by y = , on the right by the line , and above by the line y = 2 A) 25 \pi B) 25/3 \pi C) 25 /2 \pi D) 75 /2 \pi , and above by the line y = 2


A) 25 π\pi
B) 25/3 π\pi
C) 25 /2 π\pi
D) 75 /2 π\pi

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Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = 7csc x, y = 7 , \le x \le A) 49 - 98 \pi B) + 14 \pi C) 7 - 49 \pi D) 49 + 98 \pi -y = 7csc x, y = 7 Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = 7csc x, y = 7 , \le x \le A) 49 - 98 \pi B) + 14 \pi C) 7 - 49 \pi D) 49 + 98 \pi , Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = 7csc x, y = 7 , \le x \le A) 49 - 98 \pi B) + 14 \pi C) 7 - 49 \pi D) 49 + 98 \pi ≤\le x ≤\le Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = 7csc x, y = 7 , \le x \le A) 49 - 98 \pi B) + 14 \pi C) 7 - 49 \pi D) 49 + 98 \pi


A) 49 Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = 7csc x, y = 7 , \le x \le A) 49 - 98 \pi B) + 14 \pi C) 7 - 49 \pi D) 49 + 98 \pi - 98 π\pi
B) Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = 7csc x, y = 7 , \le x \le A) 49 - 98 \pi B) + 14 \pi C) 7 - 49 \pi D) 49 + 98 \pi + 14 π\pi
C) 7 Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = 7csc x, y = 7 , \le x \le A) 49 - 98 \pi B) + 14 \pi C) 7 - 49 \pi D) 49 + 98 \pi - 49 π\pi
D) 49 Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = 7csc x, y = 7 , \le x \le A) 49 - 98 \pi B) + 14 \pi C) 7 - 49 \pi D) 49 + 98 \pi + 98 π\pi

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Solve the problem. -Find a curve through the point Solve the problem. -Find a curve through the point whose length integral, 1 \le x \le 2, is A) y = B) y = 5 C) y = D) y = 5 whose length integral, 1 ≤\le x ≤\le 2, is Solve the problem. -Find a curve through the point whose length integral, 1 \le x \le 2, is A) y = B) y = 5 C) y = D) y = 5


A) y = Solve the problem. -Find a curve through the point whose length integral, 1 \le x \le 2, is A) y = B) y = 5 C) y = D) y = 5 Solve the problem. -Find a curve through the point whose length integral, 1 \le x \le 2, is A) y = B) y = 5 C) y = D) y = 5
B) y = 5 Solve the problem. -Find a curve through the point whose length integral, 1 \le x \le 2, is A) y = B) y = 5 C) y = D) y = 5
C) y = Solve the problem. -Find a curve through the point whose length integral, 1 \le x \le 2, is A) y = B) y = 5 C) y = D) y = 5 Solve the problem. -Find a curve through the point whose length integral, 1 \le x \le 2, is A) y = B) y = 5 C) y = D) y = 5
D) y = 5 Solve the problem. -Find a curve through the point whose length integral, 1 \le x \le 2, is A) y = B) y = 5 C) y = D) y = 5

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Solve the problem. -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. v = cos Solve the problem. -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. v = cos t, s(0) = 1 A) s = 2 \pi sin t B) s = sin t C) s = sin t D) s = sin t + \pi t, s(0) = 1


A) s = 2 π\pi sin Solve the problem. -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. v = cos t, s(0) = 1 A) s = 2 \pi sin t B) s = sin t C) s = sin t D) s = sin t + \pi t
B) s = sin t
C) s = Solve the problem. -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. v = cos t, s(0) = 1 A) s = 2 \pi sin t B) s = sin t C) s = sin t D) s = sin t + \pi sin Solve the problem. -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. v = cos t, s(0) = 1 A) s = 2 \pi sin t B) s = sin t C) s = sin t D) s = sin t + \pi t
D) s = Solve the problem. -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. v = cos t, s(0) = 1 A) s = 2 \pi sin t B) s = sin t C) s = sin t D) s = sin t + \pi sin Solve the problem. -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. v = cos t, s(0) = 1 A) s = 2 \pi sin t B) s = sin t C) s = sin t D) s = sin t + \pi t + π\pi

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