Question 1

Approximate the arc length of the curve   from x = 2 to x = 4.

Accepted Answer

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

Question 2

Use the Theorem of Pappus to find the volume of the solid that is generated when the region enclosed by y = 10 - x and y = x2 + 4 is rotated about the x-axis.

Accepted Answer

area = @#IMG-DLM& = 20.833333

Question 3

A flat rectangular plate, 5 feet long and 6 feet wide is submerged in water (weight density 62.4 lbs/ft3) with the 5 foot edge parallel to and 3 feet below the surface. Find the force against the surface of the plate.

Accepted Answer

Question 4

Answer true or false. The arc length of the curve   from x = -4 to x = 3 is 6.

Accepted Answer

A) True 
 B)False

Question 5

A right triangle is submerged vertically with one side at the surface in a liquid of density $\rho$. The triangle has a leg that is 9 m long located at the surface and a leg 9 m long straight down. Find the force exerted on the triangular surface, in terms of the density. Neglect the effect of the atmosphere above the liquid.

Accepted Answer

A)  243 $\rho$N 
B)  364.5 $\rho$N 
C)  121.5 $\rho$N 
D)  91.12 $\rho$N 
E)  20.25 $\rho$N 
A)  243 $\rho$N 
B)  364.5 $\rho$N 
C)  121.5 $\rho$N 
D)  91.12 $\rho$N 
E)  20.25 $\rho$N

Question 6

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y = x2, y = 1, and x = 0 is revolved about the x axis.

Accepted Answer

Question 7

Evaluate   .

Accepted Answer

The answer of Evaluate   ....

Question 8

Answer true or false. The area of the surface generated by revolving the curve y = cos x,   about the x-axis to be 8.08.

Accepted Answer

A) True 
 B)False

Question 9

Answer true or false.   = sinh-1 ex + C

Accepted Answer

A) True 
 B)False

Question 10

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y = x3, x = 1, and y = -8 is revolved about the line y = -1.

Accepted Answer

Question 11

Find the force on a 60 ft2 horizontal surface 48 ft deep in water. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.4 lb/ft3.)

Accepted Answer

Question 12

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y2 = 9x and y = x is revolved about the line x = 9.

Accepted Answer

Question 13

Find the centroid of the region enclosed by y = x3 - 2 and y = 3x + 7 from x = -1 to x = 0.

Accepted Answer

A)  (-0.477419, 1.668203) 
B)  (0.425806, 1.840246) 
C)  (1.840246, -0.477419) 
D)  (-0.477419, 1.840246) 
E)  (0.425806, 1.668203) 
A)  (-0.477419, 1.668203) 
B)  (0.425806, 1.840246) 
C)  (1.840246, -0.477419) 
D)  (-0.477419, 1.840246) 
E)  (0.425806, 1.668203)

Question 14

Answer true or false. The arc length of the curve y = (x - 1)7/2 from x = 0 to x = 2 is given by   .

Accepted Answer

A) True 
 B)False

Question 15

Evaluate cosh-1(7).

Accepted Answer

A)  0.7539 
B)  2.7687 
C)  2.4779 
D)  2.6441 
E)  2.6339 
A)  0.7539 
B)  2.7687 
C)  2.4779 
D)  2.6441 
E)  2.6339

Question 16

Find the volume of the solid generated when the region enclosed by y = x, y = 2, and x = 0 is revolved about the y-axis.

Accepted Answer

The answer of Find the volume of the solid generated...

Question 17

Use a graphing utility to find the area of the region enclosed by the curves y = x2 + 6, y = 2, x = 0, x = 2.

Accepted Answer

Question 18

Find the arc length of the curve y = 2x5/2 from x = 0 to   .

Accepted Answer

Question 19

Find the area of the region enclosed by y = 6x -x2 and y = 8.

Accepted Answer

The answer of Find the area of the region enclosed...

Question 20

Find f '(x) if f(x) = tanh - 1(6x + 9).

Accepted Answer

The answer of Find f '(x) if f(x) = tanh...

Approximate the arc length of the curve from x = 2 to x = 4.

Use the Theorem of Pappus to find the volume of the solid that is generated when the region enclosed by y = 10 - x and y = x²+ 4 is rotated about the x-axis.

A flat rectangular plate, 5 feet long and 6 feet wide is submerged in water (weight density 62.4 lbs/ft³) with the 5 foot edge parallel to and 3 feet below the surface. Find the force against the surface of the plate.

Answer true or false. The arc length of the curve from x = -4 to x = 3 is 6.

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y = x², y = 1, and x = 0 is revolved about the x axis.

Evaluate .

Answer true or false. The area of the surface generated by revolving the curve y = cos x, about the x-axis to be 8.08.

Answer true or false. = sinh^-1 e^x + C

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y = x³, x = 1, and y = -8 is revolved about the line y = -1.

Find the force on a 60 ft² horizontal surface 48 ft deep in 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 y² = 9x and y = x is revolved about the line x = 9.

Find the centroid of the region enclosed by y = x³ - 2 and y = 3x + 7 from x = -1 to x = 0.

Answer true or false. The arc length of the curve y = (x - 1)^7/2 from x = 0 to x = 2 is given by .

Evaluate cosh^-¹(7).

Find the volume of the solid generated when the region enclosed by y = x, y = 2, and x = 0 is revolved about the y-axis.

Use a graphing utility to find the area of the region enclosed by the curves y = x² + 6, y = 2, x = 0, x = 2.

Find the arc length of the curve y = 2x^5/2 from x = 0 to .

Find the area of the region enclosed by y = 6x -x² and y = 8.

Find f '(x) if f(x) = tanh ^- ¹(6x + 9).

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

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

Approximate the arc length of the curve from x = 2 to x = 4.

Use the Theorem of Pappus to find the volume of the solid that is generated when the region enclosed by y = 10 - x and y = x2 + 4 is rotated about the x-axis.

A flat rectangular plate, 5 feet long and 6 feet wide is submerged in water (weight density 62.4 lbs/ft3) with the 5 foot edge parallel to and 3 feet below the surface. Find the force against the surface of the plate.

Answer true or false. The arc length of the curve from x = -4 to x = 3 is 6.

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y = x2, y = 1, and x = 0 is revolved about the x axis.

Evaluate .

Answer true or false. The area of the surface generated by revolving the curve y = cos x, about the x-axis to be 8.08.

Answer true or false. = sinh-1 ex + C

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y = x3, x = 1, and y = -8 is revolved about the line y = -1.

Find the force on a 60 ft2 horizontal surface 48 ft deep in 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 y2 = 9x and y = x is revolved about the line x = 9.

Find the centroid of the region enclosed by y = x3 - 2 and y = 3x + 7 from x = -1 to x = 0.

Answer true or false. The arc length of the curve y = (x - 1)7/2 from x = 0 to x = 2 is given by .

Evaluate cosh-1(7).

Find the volume of the solid generated when the region enclosed by y = x, y = 2, and x = 0 is revolved about the y-axis.

Use a graphing utility to find the area of the region enclosed by the curves y = x2 + 6, y = 2, x = 0, x = 2.

Find the arc length of the curve y = 2x5/2 from x = 0 to .

Find the area of the region enclosed by y = 6x -x2 and y = 8.

Find f '(x) if f(x) = tanh - 1(6x + 9).

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

Use the Theorem of Pappus to find the volume of the solid that is generated when the region enclosed by y = 10 - x and y = x²+ 4 is rotated about the x-axis.

A flat rectangular plate, 5 feet long and 6 feet wide is submerged in water (weight density 62.4 lbs/ft³) with the 5 foot edge parallel to and 3 feet below the surface. Find the force against the surface of the plate.

Use the method of washers to find the volume of the solid that results when the area of the region enclosed by y = x², y = 1, and x = 0 is revolved about the x axis.

Answer true or false. = sinh^-1 e^x + C

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y = x³, x = 1, and y = -8 is revolved about the line y = -1.

Find the force on a 60 ft² horizontal surface 48 ft deep in 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 y² = 9x and y = x is revolved about the line x = 9.

Find the centroid of the region enclosed by y = x³ - 2 and y = 3x + 7 from x = -1 to x = 0.

Answer true or false. The arc length of the curve y = (x - 1)^7/2 from x = 0 to x = 2 is given by .

Evaluate cosh^-¹(7).

Use a graphing utility to find the area of the region enclosed by the curves y = x² + 6, y = 2, x = 0, x = 2.

Find the arc length of the curve y = 2x^5/2 from x = 0 to .

Find the area of the region enclosed by y = 6x -x² and y = 8.

Find f '(x) if f(x) = tanh ^- ¹(6x + 9).