Question 1

Find the centroid of the region bound by y = x + 2 and y = x2 - 4.

Accepted Answer

@#IMG-DLM& = @#IMG-DLM& = @#IMG-DLM& = 1.098 @#IMG-DLM& = @#IMG-DLM& =

Question 2

Liquid cement (weight density 250lbs/ft3) is poured into a form whose ends are 3 foot squares. Find the force on one end if the cement is 2 feet deep.

Accepted Answer

Question 3

Use cylindrical shells to find the volume of the solid when the region enclosed by xy = 12, x + y = 8 is revolved about the x-axis.

Accepted Answer

A)  21.332 $\pi$ 
B)  0.01 $\pi$ 
C)  10.667 $\pi$ 
D)  ( $\pi$) 
E)  21.333 $\pi$ 
A)  21.332 $\pi$ 
B)  0.01 $\pi$ 
C)  10.667 $\pi$ 
D)  ( $\pi$) 
E)  21.333 $\pi$

Question 4

Masses m1 = 6, m2 = 3, m3 = 11 are positioned on a weightless on a weightless beam as shown in the figure.   Where should be fulcrum be placed so that the beam is in equilibrium?

Accepted Answer

Moment for m₁ = 6x fo

Question 5

Find the arc length of the curve   from x = 1 to x = 2.

Accepted Answer

The answer of Find the arc length of the curve...

Question 6

Find the force on a 30-ft wide by 4-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.4 lb/ft3.)

Accepted Answer

Question 7

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y = 4x + 3, x = 2, x = 4, and y = 0 is revolved about the y-axis.

Accepted Answer

The answer of Use cylindrical shells to find the volume...

Question 8

Find the Mass of a lamina bounded by the x-axis, the line x = 4, and the curve y = x3. The density of the lamina is   = 4.

Accepted Answer

Question 9

Find the area of the surface generated when   from x = 3 to x = 6 is rotated around the x-axis.

Accepted Answer

The answer of Find the area of the surface generated...

Question 10

Find the arc length of the curve   from x = 1 to x = 2.

Accepted Answer

The answer of Find the arc length of the curve...

Question 11

A flat plate in the form of a T is submerged in water (weight density 9810 N/m3) as shown in the figure. The cross piece is 10 meters long (horizontally) and 3 meters wide (deep). The upright is 14 meters long (vertically) and 3 meters wide. Find the force on the surface when the surface of the water is 3 meters above the cross piece.

Accepted Answer

Question 12

Use cylindrical shells to find the volume of the solid when the region enclosed by x = y2, x = 0, y = 3 is revolved about the x-axis.

Accepted Answer

A)  13.5 $\pi$ 
B)  40.5 
C)  81 $\pi$ 
D)  40.5 $\pi$ 
E)  ( $\pi$) 
A)  13.5 $\pi$ 
B)  40.5 
C)  81 $\pi$ 
D)  40.5 $\pi$ 
E)  ( $\pi$)

Question 13

A cylindrical tank 6 feet in diameter and 12 feet high is filled with water weighing 62.4lbs/ft3. How much work is required to pump the water over the top of the tank?

Accepted Answer

@#IMG-DLM& = @#IMG-DLM& = @#IMG-DLM& = 4

Question 14

A bucket weighing 1000 pounds is to be lifted from the bottom of a shaft 20 feet deep. The weight of the cable used to hoist it is 20 pounds per foot. How much work is done lifting the bucket to the top of the shaft?

Accepted Answer

Total weight = weight of bucke

Question 15

A 1.9-kg object is moving at 5.5 m/s. If a force in the direction of the motion does 27.9 J of work on the object, what is the object's final speed?

Accepted Answer

A)  28.7375 m/s 
B)  7.72 m/s 
C)  56.6375 m/s 
D)  5.46 m/s 
E)  6.70 m/s 
A)  28.7375 m/s 
B)  7.72 m/s 
C)  56.6375 m/s 
D)  5.46 m/s 
E)  6.70 m/s

Question 16

A flat triangular plate whose dimensions are 17, 17, and 30 feet is submerged in water (weight density 62.4 lbs/ft3) point up so that its longer side is below the surface and parallel to it and its vertex is 4 feet below the water. Find the force against the surface of the plate.

Accepted Answer

height of triangle =

Question 17

A flat rectangular plate is submerged horizontally in water to a depth of 3.6 ft. If the top surface of the plate has an area of 30 ft2, and the liquid in which it is submerged is water, find the force on the top of the plate. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.2 lb/ft3.)

Accepted Answer

A)  108 lb 
B)  22,392 lb 
C)  1,866 lb 
D)  6,717.6 lb 
E)  671.76 lb 
A)  108 lb 
B)  22,392 lb 
C)  1,866 lb 
D)  6,717.6 lb 
E)  671.76 lb

Question 18

Answer true or false. The force a liquid of density $\rho$ exerts on an equilateral triangle with edges h in length submerged point down is given by   .

Accepted Answer

A) True 
 B)False

Question 19

Answer true or false. The force on a semicircular, vertical wall with top d is given by   . Neglect the effect of the atmosphere above the liquid and assume the liquid is at a depth equal to the height of the wall. (The letter   stands for the weight of the liquid.)

Accepted Answer

A) True 
 B)False

Question 20

Find the area of the surface generated when   from x = 0 to x = 4 is rotated around the x-axis.

Accepted Answer

The answer of Find the area of the surface generated...

Find the centroid of the region bound by y = x + 2 and y = x² - 4.

Liquid cement (weight density 250lbs/ft³) is poured into a form whose ends are 3 foot squares. Find the force on one end if the cement is 2 feet deep.

Use cylindrical shells to find the volume of the solid when the region enclosed by xy = 12, x + y = 8 is revolved about the x-axis.

Masses m₁ = 6, m₂ = 3, m₃ = 11 are positioned on a weightless on a weightless beam as shown in the figure. Where should be fulcrum be placed so that the beam is in equilibrium?

Find the arc length of the curve from x = 1 to x = 2.

Find the force on a 30-ft wide by 4-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.4 lb/ft³.)

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y = 4x + 3, x = 2, x = 4, and y = 0 is revolved about the y-axis.

Find the Mass of a lamina bounded by the x-axis, the line x = 4, and the curve y = x³. The density of the lamina is = 4.

Find the area of the surface generated when from x = 3 to x = 6 is rotated around the x-axis.

Find the arc length of the curve from x = 1 to x = 2.

Use cylindrical shells to find the volume of the solid when the region enclosed by x = y², x = 0, y = 3 is revolved about the x-axis.

A cylindrical tank 6 feet in diameter and 12 feet high is filled with water weighing 62.4lbs/ft³. How much work is required to pump the water over the top of the tank?

A bucket weighing 1000 pounds is to be lifted from the bottom of a shaft 20 feet deep. The weight of the cable used to hoist it is 20 pounds per foot. How much work is done lifting the bucket to the top of the shaft?

A 1.9-kg object is moving at 5.5 m/s. If a force in the direction of the motion does 27.9 J of work on the object, what is the object's final speed?

A flat triangular plate whose dimensions are 17, 17, and 30 feet is submerged in water (weight density 62.4 lbs/ft³) point up so that its longer side is below the surface and parallel to it and its vertex is 4 feet below the water. Find the force against the surface of the plate.

Answer true or false. The force on a semicircular, vertical wall with top d is given by . Neglect the effect of the atmosphere above the liquid and assume the liquid is at a depth equal to the height of the wall. (The letter stands for the weight of the liquid.)

Find the area of the surface generated when from x = 0 to x = 4 is rotated around the x-axis.

Limits and Continuity

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Integration

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

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Exam 6: Applications of the Definite Integral in Geometry, Science and Engineering

Find the centroid of the region bound by y = x + 2 and y = x2 - 4.

Liquid cement (weight density 250lbs/ft3) is poured into a form whose ends are 3 foot squares. Find the force on one end if the cement is 2 feet deep.

Use cylindrical shells to find the volume of the solid when the region enclosed by xy = 12, x + y = 8 is revolved about the x-axis.

Masses m1 = 6, m2 = 3, m3 = 11 are positioned on a weightless on a weightless beam as shown in the figure. Where should be fulcrum be placed so that the beam is in equilibrium?

Find the arc length of the curve from x = 1 to x = 2.

Find the force on a 30-ft wide by 4-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.4 lb/ft3.)

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y = 4x + 3, x = 2, x = 4, and y = 0 is revolved about the y-axis.

Find the Mass of a lamina bounded by the x-axis, the line x = 4, and the curve y = x3. The density of the lamina is = 4.

Find the area of the surface generated when from x = 3 to x = 6 is rotated around the x-axis.

Find the arc length of the curve from x = 1 to x = 2.

Use cylindrical shells to find the volume of the solid when the region enclosed by x = y2, x = 0, y = 3 is revolved about the x-axis.

A cylindrical tank 6 feet in diameter and 12 feet high is filled with water weighing 62.4lbs/ft3. How much work is required to pump the water over the top of the tank?

A bucket weighing 1000 pounds is to be lifted from the bottom of a shaft 20 feet deep. The weight of the cable used to hoist it is 20 pounds per foot. How much work is done lifting the bucket to the top of the shaft?

A 1.9-kg object is moving at 5.5 m/s. If a force in the direction of the motion does 27.9 J of work on the object, what is the object's final speed?

A flat triangular plate whose dimensions are 17, 17, and 30 feet is submerged in water (weight density 62.4 lbs/ft3) point up so that its longer side is below the surface and parallel to it and its vertex is 4 feet below the water. Find the force against the surface of the plate.

Answer true or false. The force a liquid of density ρ\rhoρ exerts on an equilateral triangle with edges h in length submerged point down is given by .

Answer true or false. The force on a semicircular, vertical wall with top d is given by . Neglect the effect of the atmosphere above the liquid and assume the liquid is at a depth equal to the height of the wall. (The letter stands for the weight of the liquid.)

Find the area of the surface generated when from x = 0 to x = 4 is rotated around the x-axis.

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Find the centroid of the region bound by y = x + 2 and y = x² - 4.

Liquid cement (weight density 250lbs/ft³) is poured into a form whose ends are 3 foot squares. Find the force on one end if the cement is 2 feet deep.

Masses m₁ = 6, m₂ = 3, m₃ = 11 are positioned on a weightless on a weightless beam as shown in the figure. Where should be fulcrum be placed so that the beam is in equilibrium?

Find the force on a 30-ft wide by 4-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.4 lb/ft³.)

Find the Mass of a lamina bounded by the x-axis, the line x = 4, and the curve y = x³. The density of the lamina is = 4.

Use cylindrical shells to find the volume of the solid when the region enclosed by x = y², x = 0, y = 3 is revolved about the x-axis.

A cylindrical tank 6 feet in diameter and 12 feet high is filled with water weighing 62.4lbs/ft³. How much work is required to pump the water over the top of the tank?

A flat triangular plate whose dimensions are 17, 17, and 30 feet is submerged in water (weight density 62.4 lbs/ft³) point up so that its longer side is below the surface and parallel to it and its vertex is 4 feet below the water. Find the force against the surface of the plate.