Use a graphing utility to find the area of the region enclosed by the curves y = x3 -4x2 + 3x + 1, y = 0, x = 0, x = 2. Approximate area to three decimal places.

A) 13.333 B) 7.333 C) 20.000 D) 0.333 E) 1.333 A) 13.333 B) 7.333 C) 20.000 D) 0.333 E) 1.333

Find the force (in N) on the top of a submerged object if its surface is 4.2 m2 and the pressure acting on it is 6.6 * 106 Pa. Neglect the effect of the atmosphere above the liquid.

A) 6,600,000 N B) 27,720,000 N C) 4,200,000 N D) 166.32 N E) 66,000,000 N A) 6,600,000 N B) 27,720,000 N C) 4,200,000 N D) 166.32 N E) 66,000,000 N

Find the area of the region enclosed by y = x2 and x -y + 2 = 0.

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

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

A flat plate, shaped in the form of a semicircle 10 meters in diameter is submerged in water (weight density 9810 N/m³) as shown. Find the force against the surface of the plate.

(Essay)

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Question 181

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

(Essay)

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Question 182

Use a graphing utility to find the area of the region enclosed by the curves y = x³ -4x² + 3x + 1, y = 0, x = 0, x = 2. Approximate area to three decimal places.

(Multiple Choice)

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Question 183

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves , x = 0, y = 3, y = 0 about the y-axis. Approximate area to three decimal places.

(Multiple Choice)

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Question 184

Find the work done when a constant force of 45 lb in the positive x direction moves an object from x = -2 to x = 9 ft.

(Multiple Choice)

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Question 185

Answer true or false. The area of the surface generated by revolving the curve x = t², y = t + 4, 0 $\le$ t $\le$ 1 about the x-axis is given by $Answer true or false. The area of the surface generated by revolving the curve x = t<sup>2</sup>, y = t + 4, 0 \le t \le 1 about the x-axis is given by .$ .

(True/False)

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Question 186

Answer true or false. The curves x = y² + 3 and x = 5y + 3 intersect at y = 1 and y = 2.

(True/False)

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Question 187

Find the area of the surface that is generated by revolving the portion of the curve y = x⁴ between x = 0 and x = 2 about the x-axis.

(Essay)

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Question 188

Find the centroid of a triangle with vertices (0, 0), (8, 0), and (0, 3).

(Multiple Choice)

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Question 189

A constant force of 37 lb moves an object from 2 ft to 79 ft. How much work is done in moving the object?

(Short Answer)

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Question 190

Find the area of the surface generated when y = 8 - x from x = 0 to x = 6 is rotated around the x-axis.

(Essay)

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Question 191

Find the area enclosed by the curves y = sin 5x, y = 2x + 2, x = 0, x = 5 $\pi$ . Approximate area to three decimal places.

(Multiple Choice)

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Question 192

Find the force (in N) on the top of a submerged object if its surface is 4.2 m² and the pressure acting on it is 6.6 * 10⁶ Pa. Neglect the effect of the atmosphere above the liquid.

(Multiple Choice)

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Question 193

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

(Essay)

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Question 194

A conical tank has a diameter of 6 feet and is 9 feet deep. If the tank is filled to a depth of 7 feet with water of density 62.4lbs/ft³, how much work is required to pump the water over the top?

(Essay)

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Question 195

Use the method of washers to find the volume of the solid that results when the area enclosed by y² = 16x, y = 5, and x = 7 is revolved about the x axis.

(Essay)

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Question 196

Approximate the arc length of the curve y³ = x² from (0, 0) to (64, 16). Approximate area to three decimal places.

(Essay)

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Question 197

Use cylindrical shells to find the volume of the solid when the region enclosed by , x = 8, y = 0 is revolved about the x-axis.

(Multiple Choice)

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Question 198

Find the area of the region enclosed by y = x² and x -y + 2 = 0.

(Essay)

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Question 199

Find the force on a 190 ft² horizontal surface 22 ft deep in water. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.4 lb/ft³.)

(Multiple Choice)

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Question 200

Showing 181 - 200 of 314

A flat plate, shaped in the form of a semicircle 10 meters in diameter is submerged in water (weight density 9810 N/m³) as shown. Find the force against the surface of the plate.

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

Use a graphing utility to find the area of the region enclosed by the curves y = x³ -4x² + 3x + 1, y = 0, x = 0, x = 2. Approximate area to three decimal places.

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves , x = 0, y = 3, y = 0 about the y-axis. Approximate area to three decimal places.

Find the work done when a constant force of 45 lb in the positive x direction moves an object from x = -2 to x = 9 ft.

Answer true or false. The curves x = y² + 3 and x = 5y + 3 intersect at y = 1 and y = 2.

Find the area of the surface that is generated by revolving the portion of the curve y = x⁴ between x = 0 and x = 2 about the x-axis.

Find the centroid of a triangle with vertices (0, 0), (8, 0), and (0, 3).

A constant force of 37 lb moves an object from 2 ft to 79 ft. How much work is done in moving the object?

Find the area of the surface generated when y = 8 - x from x = 0 to x = 6 is rotated around the x-axis.

Find the area enclosed by the curves y = sin 5x, y = 2x + 2, x = 0, x = 5 $\pi$ . Approximate area to three decimal places.

Find the force (in N) on the top of a submerged object if its surface is 4.2 m² and the pressure acting on it is 6.6 * 10⁶ Pa. Neglect the effect of the atmosphere above the liquid.

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

A conical tank has a diameter of 6 feet and is 9 feet deep. If the tank is filled to a depth of 7 feet with water of density 62.4lbs/ft³, how much work is required to pump the water over the top?

Use the method of washers to find the volume of the solid that results when the area enclosed by y² = 16x, y = 5, and x = 7 is revolved about the x axis.

Approximate the arc length of the curve y³ = x² from (0, 0) to (64, 16). Approximate area to three decimal places.

Use cylindrical shells to find the volume of the solid when the region enclosed by , x = 8, y = 0 is revolved about the x-axis.

Find the area of the region enclosed by y = x² and x -y + 2 = 0.

Find the force on a 190 ft² horizontal surface 22 ft deep in water. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.4 lb/ft³.)

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

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Topics in Vector Calculus

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

A flat plate, shaped in the form of a semicircle 10 meters in diameter is submerged in water (weight density 9810 N/m3) as shown. Find the force against the surface of the plate.

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

Use a graphing utility to find the area of the region enclosed by the curves y = x3 -4x2 + 3x + 1, y = 0, x = 0, x = 2. Approximate area to three decimal places.

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves , x = 0, y = 3, y = 0 about the y-axis. Approximate area to three decimal places.

Find the work done when a constant force of 45 lb in the positive x direction moves an object from x = -2 to x = 9 ft.

Answer true or false. The area of the surface generated by revolving the curve x = t2, y = t + 4, 0 ≤\le≤ t ≤\le≤ 1 about the x-axis is given by .

Answer true or false. The curves x = y2 + 3 and x = 5y + 3 intersect at y = 1 and y = 2.

Find the area of the surface that is generated by revolving the portion of the curve y = x4 between x = 0 and x = 2 about the x-axis.

Find the centroid of a triangle with vertices (0, 0), (8, 0), and (0, 3).

A constant force of 37 lb moves an object from 2 ft to 79 ft. How much work is done in moving the object?

Find the area of the surface generated when y = 8 - x from x = 0 to x = 6 is rotated around the x-axis.

Find the area enclosed by the curves y = sin 5x, y = 2x + 2, x = 0, x = 5 π\piπ . Approximate area to three decimal places.

Find the force (in N) on the top of a submerged object if its surface is 4.2 m2 and the pressure acting on it is 6.6 * 106 Pa. Neglect the effect of the atmosphere above the liquid.

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

A conical tank has a diameter of 6 feet and is 9 feet deep. If the tank is filled to a depth of 7 feet with water of density 62.4lbs/ft3, how much work is required to pump the water over the top?

Use the method of washers to find the volume of the solid that results when the area enclosed by y2 = 16x, y = 5, and x = 7 is revolved about the x axis.

Approximate the arc length of the curve y3 = x2 from (0, 0) to (64, 16). Approximate area to three decimal places.

Use cylindrical shells to find the volume of the solid when the region enclosed by , x = 8, y = 0 is revolved about the x-axis.

Find the area of the region enclosed by y = x2 and x -y + 2 = 0.

Find the force on a 190 ft2 horizontal surface 22 ft deep in water. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.4 lb/ft3.)

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

A flat plate, shaped in the form of a semicircle 10 meters in diameter is submerged in water (weight density 9810 N/m³) as shown. Find the force against the surface of the plate.

Use a graphing utility to find the area of the region enclosed by the curves y = x³ -4x² + 3x + 1, y = 0, x = 0, x = 2. Approximate area to three decimal places.

Answer true or false. The curves x = y² + 3 and x = 5y + 3 intersect at y = 1 and y = 2.

Find the area of the surface that is generated by revolving the portion of the curve y = x⁴ between x = 0 and x = 2 about the x-axis.

Find the area enclosed by the curves y = sin 5x, y = 2x + 2, x = 0, x = 5 $\pi$ . Approximate area to three decimal places.

Find the force (in N) on the top of a submerged object if its surface is 4.2 m² and the pressure acting on it is 6.6 * 10⁶ Pa. Neglect the effect of the atmosphere above the liquid.

A conical tank has a diameter of 6 feet and is 9 feet deep. If the tank is filled to a depth of 7 feet with water of density 62.4lbs/ft³, how much work is required to pump the water over the top?

Use the method of washers to find the volume of the solid that results when the area enclosed by y² = 16x, y = 5, and x = 7 is revolved about the x axis.

Approximate the arc length of the curve y³ = x² from (0, 0) to (64, 16). Approximate area to three decimal places.

Find the area of the region enclosed by y = x² and x -y + 2 = 0.

Find the force on a 190 ft² horizontal surface 22 ft deep in water. Neglect the effect of the atmosphere above the liquid. (The density of water is 62.4 lb/ft³.)