Exam 7: Applications of the Integral

A spring in equilibrium is 10 inches long and an external force of 30 pounds stretches the spring to a length of 18 inches. The work done by the spring in stretching it from equilibrium to 12 inches, in inch-pounds, is

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Question 81

By the Pappus Theorem, the volume of the solid formed by revolving the region enclosed by the circle $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 1$ about the x-axis is

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Question 82

A trough whose cross-section is a right isosceles triangle whose base is 6 feet long and altitude is 4 feet long 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

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Question 83

A trough whose cross-section is a trapezoid whose lower base is 4 feet long and upper base is 6 feet long, and is 1 foot high 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

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Question 84

A trough whose cross-section is a right isosceles triangle whose base is 4 feet long and altitude is 4 feet long 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

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Question 85

The arc length of $y = - ( x + 1 ) ^ { \frac { 3 } { 2 } } + 1 \text { for } x \in [ 1,8 ]$ is

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Question 86

Three particles having masses 1, 2, and 3 kg are located on the x-axis at 3,1,-1 respectively. The center of mass of this system is located at x =

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Question 87

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

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Question 88

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

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Question 89

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

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Question 90

A tank in the form of an inverted right circular cone is 8 meters across the top and 16 meters deep. The tank is filled with a liquid with the height of 8 meters weighing 950 kg/cu m. The work done, in Newton-meters, of pumping all the liquid out is

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Question 91

A cylindrical sewer pipe of radius 1 foot 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

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Question 92

The work done by a winch winding in a 120-foot chain weighing 240 pounds, in foot-pounds, is

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Question 93

Let V be the volume of the solid generated by revolving the region enclosed by y = -x³, y = x³ - 2x²; about the y-axis. Then V is

(Multiple Choice)

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Question 94

A trough whose cross-section is a trapezoid whose lower base is 4 feet long, upper base is 8 feet long, and is 4 feet high 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 95

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

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Question 96

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

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Question 97

Let V be the volume of the solid generated by revolving the region enclosed by $y = \sqrt { x },$ the x-axis, $x = 4;$ about the y-axis. Then V is

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Question 98

The arc length of $y = \ln ( \sec x ) \text { for } x \in \left[ 0 , \frac { \pi } { 4 } \right]$ is

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Question 99

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

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Question 100

Showing 81 - 100 of 163

A spring in equilibrium is 10 inches long and an external force of 30 pounds stretches the spring to a length of 18 inches. The work done by the spring in stretching it from equilibrium to 12 inches, in inch-pounds, is

By the Pappus Theorem, the volume of the solid formed by revolving the region enclosed by the circle $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 1$ about the x-axis is

A trough whose cross-section is a right isosceles triangle whose base is 6 feet long and altitude is 4 feet long 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

A trough whose cross-section is a trapezoid whose lower base is 4 feet long and upper base is 6 feet long, and is 1 foot high 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

A trough whose cross-section is a right isosceles triangle whose base is 4 feet long and altitude is 4 feet long 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

The arc length of $y = - ( x + 1 ) ^ { \frac { 3 } { 2 } } + 1 \text { for } x \in [ 1,8 ]$ is

Three particles having masses 1, 2, and 3 kg are located on the x-axis at 3,1,-1 respectively. The center of mass of this system is located at x =

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

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

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

A tank in the form of an inverted right circular cone is 8 meters across the top and 16 meters deep. The tank is filled with a liquid with the height of 8 meters weighing 950 kg/cu m. The work done, in Newton-meters, of pumping all the liquid out is

A cylindrical sewer pipe of radius 1 foot 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

The work done by a winch winding in a 120-foot chain weighing 240 pounds, in foot-pounds, is

Let V be the volume of the solid generated by revolving the region enclosed by y = -x³, y = x³ - 2x²; about the y-axis. Then V is

A trough whose cross-section is a trapezoid whose lower base is 4 feet long, upper base is 8 feet long, and is 4 feet high 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 x-axis. Then V is

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

Let V be the volume of the solid generated by revolving the region enclosed by $y = \sqrt { x },$ the x-axis, $x = 4;$ about the y-axis. Then V is

The arc length of $y = \ln ( \sec x ) \text { for } x \in \left[ 0 , \frac { \pi } { 4 } \right]$ is

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

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Exam 7: Applications of the Integral

A spring in equilibrium is 10 inches long and an external force of 30 pounds stretches the spring to a length of 18 inches. The work done by the spring in stretching it from equilibrium to 12 inches, in inch-pounds, is ​

By the Pappus Theorem, the volume of the solid formed by revolving the region enclosed by the circle x2+(y−2)2=1x ^ { 2 } + ( y - 2 ) ^ { 2 } = 1x2+(y−2)2=1 about the x-axis is

A trough whose cross-section is a right isosceles triangle whose base is 6 feet long and altitude is 4 feet long 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

A trough whose cross-section is a trapezoid whose lower base is 4 feet long and upper base is 6 feet long, and is 1 foot high 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

A trough whose cross-section is a right isosceles triangle whose base is 4 feet long and altitude is 4 feet long 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

The arc length of y=−(x+1)32+1 for x∈[1,8]y = - ( x + 1 ) ^ { \frac { 3 } { 2 } } + 1 \text { for } x \in [ 1,8 ]y=−(x+1)23​+1 for x∈[1,8] is

Three particles having masses 1, 2, and 3 kg are located on the x-axis at 3,1,-1 respectively. The center of mass of this system is located at x =

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

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

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

A tank in the form of an inverted right circular cone is 8 meters across the top and 16 meters deep. The tank is filled with a liquid with the height of 8 meters weighing 950 kg/cu m. The work done, in Newton-meters, of pumping all the liquid out is

A cylindrical sewer pipe of radius 1 foot 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

The work done by a winch winding in a 120-foot chain weighing 240 pounds, in foot-pounds, is ​

Let V be the volume of the solid generated by revolving the region enclosed by y = -x3, y = x3 - 2x2; about the y-axis. Then V is

A trough whose cross-section is a trapezoid whose lower base is 4 feet long, upper base is 8 feet long, and is 4 feet high 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 x-axis. Then V is

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

Let V be the volume of the solid generated by revolving the region enclosed by y=x,y = \sqrt { x },y=x​, the x-axis, x=4;x = 4;x=4; about the y-axis. Then V is

The arc length of y=ln⁡(sec⁡x) for x∈[0,π4]y = \ln ( \sec x ) \text { for } x \in \left[ 0 , \frac { \pi } { 4 } \right]y=ln(secx) for x∈[0,4π​] is

Let V be the volume of the solid generated by revolving the region enclosed by y = x2, y = x + 2; 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

A spring in equilibrium is 10 inches long and an external force of 30 pounds stretches the spring to a length of 18 inches. The work done by the spring in stretching it from equilibrium to 12 inches, in inch-pounds, is

By the Pappus Theorem, the volume of the solid formed by revolving the region enclosed by the circle $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 1$ about the x-axis is

The arc length of $y = - ( x + 1 ) ^ { \frac { 3 } { 2 } } + 1 \text { for } x \in [ 1,8 ]$ is

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

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

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

The work done by a winch winding in a 120-foot chain weighing 240 pounds, in foot-pounds, is

Let V be the volume of the solid generated by revolving the region enclosed by y = -x³, y = x³ - 2x²; about the y-axis. Then V is

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

Let V be the volume of the solid generated by revolving the region enclosed by $y = \sqrt { x },$ the x-axis, $x = 4;$ about the y-axis. Then V is

The arc length of $y = \ln ( \sec x ) \text { for } x \in \left[ 0 , \frac { \pi } { 4 } \right]$ is

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