Let A denote the area enclosed by the equations y = x3 and y = x. Then A is

A) $\frac { 1 } { 2 }$ B) 1 C) $\frac { 3 } { 2 }$ D) 2 E) $\frac { 5 } { 2 }$ A) $\frac { 1 } { 2 }$ B) 1 C) $\frac { 3 } { 2 }$ D) 2 E) $\frac { 5 } { 2 }$

Exam 7: Applications of the Integral

Let V be the volume of the solid that lies between planes perpendicular to the x-axis from x = 0 to x = 3. The cross-sections of this solid perpendicular to the x-axis run from $y = \frac { x ^ { 2 } } { 9 }$ to $y = \sqrt { \frac { x } { 3 } }$ and they are semicircles with diameters in the xy-plane. Then V is

(Multiple Choice)

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Question 61

Let A denote the area enclosed by the equation $y = 4 - | x |$ and the x-axis. Then A is

(Multiple Choice)

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Question 62

A bucket weighing 10 pounds containing 30 pounds of sand is attached to the lower end of a chain of 100 feet long and weighs 10 pounds. The work done to lift the bucket to the top, in foot-pounds, is

(Multiple Choice)

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Question 63

A trough cross-section is a 2-foot-high and 2-foot-wide rectangle. If the trough is filled with water of density 62.5 pounds per cubic foot, the force, in pounds, due to hydrostatic pressure on one end of the trough is

(Multiple Choice)

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Question 64

Let V be the volume of the solid generated by revolving the region enclosed by about the y-axis. Then V is

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Question 65

Let V be the volume of the solid generated by revolving the region enclosed by x = y², x = 2y - y²; about the x-axis. Then V is

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Question 66

Let A denote the area enclosed by the equations $y = x ^ { 2 }$ and $y = 6 x - x ^ { 2 }$ Then A is

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Question 67

Let $\bar { y }$ denote the y-coordinate of the centroid of the region enclosed by $y = 1 - x ^ { 2 }$ and $y = 0$ Then $\bar { y }$ =

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Question 68

The work done by a variable force $F ( x ) = 40 - x$ Newtons that moves an object along a straight line in the direction of F from x = 5 meters to x = 20 meters, in Newton-meters, is

(Multiple Choice)

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Question 69

Let A denote the area enclosed by the equation $y = \sin x$ and the x-axis with $x \in [ 0 , \pi ]$ Then A is

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Question 70

Let A denote the area enclosed by the equations y = x³ and y = x. Then A is

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Question 71

The arc length of $y = ( x - 2 ) ^ { \frac { 3 } { 2 } } - 1 \text { for } x \in [ 3,6 ]$ is

(Multiple Choice)

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Question 72

Let V be the volume of the solid generated by revolving the region enclosed by $y = 3 x ^ { 2 },$ the x-axis, $x = 1 ;$ about the x-axis. Then V is

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Question 73

Let V be the volume of the solid generated by revolving the region enclosed by $y = \sqrt { \sin x },$ the y-axis, about the x-axis. Then V is

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Question 74

A right circular cylindrical water tank with height 5 meters and radius 2 meters is filled with water with density 1000 kg per cubic meter, which is 3 meters deep. The work done, in kg-meters, to remove the water from the tank is

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Question 75

Let V be the volume of the solid generated by revolving the region enclosed by x = y³, x = 2y² - y³; about the x-axis. Then V is

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Question 76

A cylindrical sewer pipe of radius 2 feet is half full of water of density 62.5 pounds per cubic foot. A gate used to seal off the sewer is placed perpendicular to the pipe opening. The force, in pounds, due to hydrostatic pressure on one end of the gate is

(Multiple Choice)

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Question 77

Let $\bar { x }$ denote the x-coordinate of the centroid of the region enclosed by $x = 2 y - y ^ { 2 }$ and $x = 0 .$ Then $\bar { x }$ =

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Question 78

A trough cross-section is a 4-foot-high and 2-foot-wide rectangle. If the trough is filled with water of density 62.5 pounds per cubic foot, the force, in pounds, due to hydrostatic pressure on one end of the trough is

(Multiple Choice)

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Question 79

Let V be the volume of the solid generated by revolving the region enclosed by x = -y², x = y² - 2y; about the x-axis. Then V is

(Multiple Choice)

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Question 80

Let A denote the area enclosed by the equation $y = 4 - | x |$ and the x-axis. Then A is

A bucket weighing 10 pounds containing 30 pounds of sand is attached to the lower end of a chain of 100 feet long and weighs 10 pounds. The work done to lift the bucket to the top, in foot-pounds, is

A trough cross-section is a 2-foot-high and 2-foot-wide rectangle. If the trough is filled with water of density 62.5 pounds per cubic foot, the force, in pounds, due to hydrostatic pressure on one end of the trough is

Let V be the volume of the solid generated by revolving the region enclosed by about the y-axis. Then V is

Let V be the volume of the solid generated by revolving the region enclosed by x = y², x = 2y - y²; about the x-axis. Then V is

Let A denote the area enclosed by the equations $y = x ^ { 2 }$ and $y = 6 x - x ^ { 2 }$ Then A is

Let $\bar { y }$ denote the y-coordinate of the centroid of the region enclosed by $y = 1 - x ^ { 2 }$ and $y = 0$ Then $\bar { y }$ =

The work done by a variable force $F ( x ) = 40 - x$ Newtons that moves an object along a straight line in the direction of F from x = 5 meters to x = 20 meters, in Newton-meters, is

Let A denote the area enclosed by the equation $y = \sin x$ and the x-axis with $x \in [ 0 , \pi ]$ Then A is

Let A denote the area enclosed by the equations y = x³ and y = x. Then A is

The arc length of $y = ( x - 2 ) ^ { \frac { 3 } { 2 } } - 1 \text { for } x \in [ 3,6 ]$ is

Let V be the volume of the solid generated by revolving the region enclosed by $y = 3 x ^ { 2 },$ the x-axis, $x = 1 ;$ about the x-axis. Then V is

Let V be the volume of the solid generated by revolving the region enclosed by $y = \sqrt { \sin x },$ the y-axis, about the x-axis. Then V is

A right circular cylindrical water tank with height 5 meters and radius 2 meters is filled with water with density 1000 kg per cubic meter, which is 3 meters deep. The work done, in kg-meters, to remove the water from the tank is

Let V be the volume of the solid generated by revolving the region enclosed by x = y³, x = 2y² - y³; about the x-axis. Then V is

A cylindrical sewer pipe of radius 2 feet is half full of water of density 62.5 pounds per cubic foot. A gate used to seal off the sewer is placed perpendicular to the pipe opening. The force, in pounds, due to hydrostatic pressure on one end of the gate is

Let $\bar { x }$ denote the x-coordinate of the centroid of the region enclosed by $x = 2 y - y ^ { 2 }$ and $x = 0 .$ Then $\bar { x }$ =

A trough cross-section is a 4-foot-high and 2-foot-wide rectangle. If the trough is filled with water of density 62.5 pounds per cubic foot, the force, in pounds, due to hydrostatic pressure on one end of the trough is

Let V be the volume of the solid generated by revolving the region enclosed by x = -y², x = y² - 2y; about the x-axis. Then V is

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Exam 7: Applications of the Integral

Let A denote the area enclosed by the equation y=4−∣x∣y = 4 - | x |y=4−∣x∣ and the x-axis. Then A is

A bucket weighing 10 pounds containing 30 pounds of sand is attached to the lower end of a chain of 100 feet long and weighs 10 pounds. The work done to lift the bucket to the top, in foot-pounds, is

A trough cross-section is a 2-foot-high and 2-foot-wide rectangle. If the trough is filled with water of density 62.5 pounds per cubic foot, the force, in pounds, due to hydrostatic pressure on one end of the trough is

Let V be the volume of the solid generated by revolving the region enclosed by about the y-axis. Then V is

Let V be the volume of the solid generated by revolving the region enclosed by x = y2, x = 2y - y2; about the x-axis. Then V is

Let A denote the area enclosed by the equations y=x2y = x ^ { 2 }y=x2 and y=6x−x2y = 6 x - x ^ { 2 }y=6x−x2 Then A is

Let yˉ\bar { y }yˉ​ denote the y-coordinate of the centroid of the region enclosed by y=1−x2y = 1 - x ^ { 2 }y=1−x2 and y=0y = 0y=0 Then yˉ\bar { y }yˉ​ =

The work done by a variable force F(x)=40−xF ( x ) = 40 - xF(x)=40−x Newtons that moves an object along a straight line in the direction of F from x = 5 meters to x = 20 meters, in Newton-meters, is

Let A denote the area enclosed by the equation y=sin⁡xy = \sin xy=sinx and the x-axis with x∈[0,π]x \in [ 0 , \pi ]x∈[0,π] Then A is

Let A denote the area enclosed by the equations y = x3 and y = x. Then A is

The arc length of y=(x−2)32−1 for x∈[3,6]y = ( x - 2 ) ^ { \frac { 3 } { 2 } } - 1 \text { for } x \in [ 3,6 ]y=(x−2)23​−1 for x∈[3,6] is

Let V be the volume of the solid generated by revolving the region enclosed by y=3x2,y = 3 x ^ { 2 },y=3x2, the x-axis, x=1;x = 1 ;x=1; about the x-axis. Then V is

Let V be the volume of the solid generated by revolving the region enclosed by y=sin⁡x,y = \sqrt { \sin x },y=sinx​, the y-axis, about the x-axis. Then V is

A right circular cylindrical water tank with height 5 meters and radius 2 meters is filled with water with density 1000 kg per cubic meter, which is 3 meters deep. The work done, in kg-meters, to remove the water from the tank is

Let V be the volume of the solid generated by revolving the region enclosed by x = y3, x = 2y2 - y3; about the x-axis. Then V is

A cylindrical sewer pipe of radius 2 feet is half full of water of density 62.5 pounds per cubic foot. A gate used to seal off the sewer is placed perpendicular to the pipe opening. The force, in pounds, due to hydrostatic pressure on one end of the gate is

Let xˉ\bar { x }xˉ denote the x-coordinate of the centroid of the region enclosed by x=2y−y2x = 2 y - y ^ { 2 }x=2y−y2 and x=0.x = 0 .x=0. Then xˉ\bar { x }xˉ =

A trough cross-section is a 4-foot-high and 2-foot-wide rectangle. If the trough is filled with water of density 62.5 pounds per cubic foot, the force, in pounds, due to hydrostatic pressure on one end of the trough is ​

Let V be the volume of the solid generated by revolving the region enclosed by x = -y2, x = y2 - 2y; about the x-axis. Then V is

Preparing for Calculus

Limits and Continuity

The Derivative

More About Derivatives

Applications of the Derivative

The Integral

Techniques of Integration

Infinite Series

Parametric Equations; Polar Equations

Vectors; Lines, Planes, and Quadric Surfaces in Space

Vector Functions

Functions of Several Variables

Directional Derivatives, Gradients, and Extrema

Multiple Integrals

Vector Calculus

Differential Equations

Filters

Let A denote the area enclosed by the equation $y = 4 - | x |$ and the x-axis. Then A is

Let V be the volume of the solid generated by revolving the region enclosed by x = y², x = 2y - y²; about the x-axis. Then V is

Let A denote the area enclosed by the equations $y = x ^ { 2 }$ and $y = 6 x - x ^ { 2 }$ Then A is

Let $\bar { y }$ denote the y-coordinate of the centroid of the region enclosed by $y = 1 - x ^ { 2 }$ and $y = 0$ Then $\bar { y }$ =

The work done by a variable force $F ( x ) = 40 - x$ Newtons that moves an object along a straight line in the direction of F from x = 5 meters to x = 20 meters, in Newton-meters, is

Let A denote the area enclosed by the equation $y = \sin x$ and the x-axis with $x \in [ 0 , \pi ]$ Then A is

Let A denote the area enclosed by the equations y = x³ and y = x. Then A is

The arc length of $y = ( x - 2 ) ^ { \frac { 3 } { 2 } } - 1 \text { for } x \in [ 3,6 ]$ is

Let V be the volume of the solid generated by revolving the region enclosed by $y = 3 x ^ { 2 },$ the x-axis, $x = 1 ;$ about the x-axis. Then V is

Let V be the volume of the solid generated by revolving the region enclosed by $y = \sqrt { \sin x },$ the y-axis, about the x-axis. Then V is

Let V be the volume of the solid generated by revolving the region enclosed by x = y³, x = 2y² - y³; about the x-axis. Then V is

Let $\bar { x }$ denote the x-coordinate of the centroid of the region enclosed by $x = 2 y - y ^ { 2 }$ and $x = 0 .$ Then $\bar { x }$ =

A trough cross-section is a 4-foot-high and 2-foot-wide rectangle. If the trough is filled with water of density 62.5 pounds per cubic foot, the force, in pounds, due to hydrostatic pressure on one end of the trough is

Let V be the volume of the solid generated by revolving the region enclosed by x = -y², x = y² - 2y; about the x-axis. Then V is