Use a graphing utility to find the area enclosed by the curves y = x3, y = x, x = 2, and x = 4. Approximate area to two decimal places.

A) 56 B) 2 C) 54 D) 17.33 E) 1 A) 56 B) 2 C) 54 D) 17.33 E) 1

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

Find f '(x) if f(x) = sinh - 1(sin 9x).

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

Find the area of the region enclosed by x = y2 - 3 and x = 5-y2.

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

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

Find the area of the surface generated by revolving x = 5y, 0 $\le$ y $\le$ 1 about the y-axis. Approximate area to three decimal places.

(Multiple Choice)

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Question 41

A swimming pool is 35 feet long and 20 feet wide. The bottom is flat but inclined as shown in the figure. The water is 7 feet deep on one end and 3 feet deep on the other. Find the force on one of the sides when the pool is filled with water (weight density 62.4 lbs/ft³).

(Essay)

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Question 42

Use a graphing utility to find the area of the region enclosed by the curves x = y⁷, x = y.

(Essay)

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Question 43

Approximate the arc length of y = cos x + 5 sin x from x = 0 to x = $\pi$ .

(Multiple Choice)

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Question 44

Find the centroid of the region enclosed by the graphs of , x = y , and y = 4.

(Essay)

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Question 45

Find the force on a 44-ft wide by 5-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft³.)

(Multiple Choice)

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Question 46

Use a graphing utility to find the area enclosed by the curves y = x³, y = x, x = 2, and x = 4. Approximate area to two decimal places.

(Multiple Choice)

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Question 47

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, y = 2 about the x-axis. Approximate area to three decimal places.

(Multiple Choice)

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Question 48

Find the area of the surface generated by revolving y = 3x, 0 $\le$ x $\le$ 1 about the x-axis. Approximate area to three decimal places.

(Multiple Choice)

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Question 49

A cylindrical tank is to be filled with gasoline weighing 50lbs/ft³. If the tank is 20 feet high and 8 feet in diameter, how much work is done by the pump in filling the tank through a hole in the bottom of the tank?

(Essay)

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Question 50

Find f '(x) if .

(Short Answer)

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Question 51

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y = x², y = 4, and x = 0 is revolved about the x-axis.

(Essay)

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Question 52

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

(Essay)

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Question 53

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y² = x³, x = 3, and y = 0 is revolved about the x axis.

(Essay)

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Question 54

Find f '(x) if f(x) = sinh ^- ¹(sin 9x).

(Short Answer)

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Question 55

Find the arc length of the curve from y = 1 to y = 8.

(Essay)

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Question 56

Find the work done when a constant force of 50 lb in the positive x direction moves an object from x = -5 to x = 7 ft.

(Short Answer)

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Question 57

Find the area of the region enclosed by x = y² - 3 and x = 5-y².

(Essay)

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Question 58

Answer true or false. If a completely full conical tank is inverted, the total force on the side wall will be the same.

(True/False)

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Question 59

Use a graphing utility to find the area of the region enclosed by the curves y = x⁹, y = 0, x = -2, x = 2.

(Essay)

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Question 60

Showing 41 - 60 of 314

Find the area of the surface generated by revolving x = 5y, 0 $\le$ y $\le$ 1 about the y-axis. Approximate area to three decimal places.

A swimming pool is 35 feet long and 20 feet wide. The bottom is flat but inclined as shown in the figure. The water is 7 feet deep on one end and 3 feet deep on the other. Find the force on one of the sides when the pool is filled with water (weight density 62.4 lbs/ft³).

Use a graphing utility to find the area of the region enclosed by the curves x = y⁷, x = y.

Approximate the arc length of y = cos x + 5 sin x from x = 0 to x = $\pi$ .

Find the centroid of the region enclosed by the graphs of , x = y , and y = 4.

Find the force on a 44-ft wide by 5-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft³.)

Use a graphing utility to find the area enclosed by the curves y = x³, y = x, x = 2, and x = 4. Approximate area to two decimal places.

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, y = 2 about the x-axis. Approximate area to three decimal places.

Find the area of the surface generated by revolving y = 3x, 0 $\le$ x $\le$ 1 about the x-axis. Approximate area to three decimal places.

A cylindrical tank is to be filled with gasoline weighing 50lbs/ft³. If the tank is 20 feet high and 8 feet in diameter, how much work is done by the pump in filling the tank through a hole in the bottom of the tank?

Find f '(x) if .

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y = x², y = 4, and x = 0 is revolved about the x-axis.

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

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y² = x³, x = 3, and y = 0 is revolved about the x axis.

Find f '(x) if f(x) = sinh ^- ¹(sin 9x).

Find the arc length of the curve from y = 1 to y = 8.

Find the work done when a constant force of 50 lb in the positive x direction moves an object from x = -5 to x = 7 ft.

Find the area of the region enclosed by x = y² - 3 and x = 5-y².

Answer true or false. If a completely full conical tank is inverted, the total force on the side wall will be the same.

Use a graphing utility to find the area of the region enclosed by the curves y = x⁹, y = 0, x = -2, x = 2.

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

Find the area of the surface generated by revolving x = 5y, 0 ≤\le≤ y ≤\le≤ 1 about the y-axis. Approximate area to three decimal places.

A swimming pool is 35 feet long and 20 feet wide. The bottom is flat but inclined as shown in the figure. The water is 7 feet deep on one end and 3 feet deep on the other. Find the force on one of the sides when the pool is filled with water (weight density 62.4 lbs/ft3).

Use a graphing utility to find the area of the region enclosed by the curves x = y7, x = y.

Approximate the arc length of y = cos x + 5 sin x from x = 0 to x = π\piπ .

Find the centroid of the region enclosed by the graphs of , x = y , and y = 4.

Find the force on a 44-ft wide by 5-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft3.)

Use a graphing utility to find the area enclosed by the curves y = x3, y = x, x = 2, and x = 4. Approximate area to two decimal places.

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves y = 4 - 2x2, y = 0, x = 0, y = 2 about the x-axis. Approximate area to three decimal places.

Find the area of the surface generated by revolving y = 3x, 0 ≤\le≤ x ≤\le≤ 1 about the x-axis. Approximate area to three decimal places.

A cylindrical tank is to be filled with gasoline weighing 50lbs/ft3. If the tank is 20 feet high and 8 feet in diameter, how much work is done by the pump in filling the tank through a hole in the bottom of the tank?

Find f '(x) if .

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y = x2, y = 4, and x = 0 is revolved about the x-axis.

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

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y2 = x3, x = 3, and y = 0 is revolved about the x axis.

Find f '(x) if f(x) = sinh - 1(sin 9x).

Find the arc length of the curve from y = 1 to y = 8.

Find the work done when a constant force of 50 lb in the positive x direction moves an object from x = -5 to x = 7 ft.

Find the area of the region enclosed by x = y2 - 3 and x = 5-y2.

Answer true or false. If a completely full conical tank is inverted, the total force on the side wall will be the same.

Use a graphing utility to find the area of the region enclosed by the curves y = x9, y = 0, x = -2, x = 2.

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 area of the surface generated by revolving x = 5y, 0 $\le$ y $\le$ 1 about the y-axis. Approximate area to three decimal places.

A swimming pool is 35 feet long and 20 feet wide. The bottom is flat but inclined as shown in the figure. The water is 7 feet deep on one end and 3 feet deep on the other. Find the force on one of the sides when the pool is filled with water (weight density 62.4 lbs/ft³).

Use a graphing utility to find the area of the region enclosed by the curves x = y⁷, x = y.

Approximate the arc length of y = cos x + 5 sin x from x = 0 to x = $\pi$ .

Find the force on a 44-ft wide by 5-ft deep wall of a swimming pool filled with water. Neglect the effect of the atmosphere above the liquid. (The weight density of water is 62.4 lb/ft³.)

Use a graphing utility to find the area enclosed by the curves y = x³, y = x, x = 2, and x = 4. Approximate area to two decimal places.

Use the method of disks to find the volume of the solid that results by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, y = 2 about the x-axis. Approximate area to three decimal places.

Find the area of the surface generated by revolving y = 3x, 0 $\le$ x $\le$ 1 about the x-axis. Approximate area to three decimal places.

A cylindrical tank is to be filled with gasoline weighing 50lbs/ft³. If the tank is 20 feet high and 8 feet in diameter, how much work is done by the pump in filling the tank through a hole in the bottom of the tank?

Use cylindrical shells to find the volume of the solid that results when the area of the region enclosed by y = x², y = 4, and x = 0 is revolved about the x-axis.

Use the method of disks to find the volume of the solid that results when the area of the region enclosed by y² = x³, x = 3, and y = 0 is revolved about the x axis.

Find f '(x) if f(x) = sinh ^- ¹(sin 9x).

Find the area of the region enclosed by x = y² - 3 and x = 5-y².

Use a graphing utility to find the area of the region enclosed by the curves y = x⁹, y = 0, x = -2, x = 2.