Exam 6: Applications of Integration

Solve the problem. -A water tank is shaped like an inverted cone with height 18 m and base radius 3 m (see figure). If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank? Express the answer in terms of $\pi$ . $Solve the problem. -A water tank is shaped like an inverted cone with height 18 m and base radius 3 m (see figure). If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank? Express the answer in terms of \pi .$

(Multiple Choice)

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Question 61

Set up an integral for the length of the curve. -y = $Set up an integral for the length of the curve. -y = , 0 \le x \le 1$ , 0 $\le$ x $\le$ 1

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Question 62

Solve the problem. -A right circular cylinder is obtained by revolving the region enclosed by the line x = r, the x-axis, and the line about the y-axis. Find the volume of the cylinder.

(Multiple Choice)

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Question 63

Find the area enclosed by the given curves. -Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the line above left by y = x + 4, and above right by y = - + 10.

(Multiple Choice)

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Question 64

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the y-axis

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Question 65

Find the length of the curve. -y = ( - 2 ) from x = 1 to x = 8

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Question 66

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the $Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = , y = 0, 0 \le x \le$ -y = $Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = , y = 0, 0 \le x \le$ , y = 0, 0 $\le$ x $\le$ $Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = , y = 0, 0 \le x \le$

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Question 67

A 1.5-mm layer of paint is applied to one side of the following surfaces. Find the volume of paint needed. Assume that x and y are measured in meters. -The spherical zone generated when the curve y = on the interval [ 4, 7] is revolved about the x-axis.

(Multiple Choice)

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Question 68

Solve the problem. -The disk $Solve the problem. -The disk + \le 1 is revolved about the y-axis to generate a torus. Find its volume. (Hint: = \pi , since it is the area of a semicircle of radius 1.)$ + $Solve the problem. -The disk + \le 1 is revolved about the y-axis to generate a torus. Find its volume. (Hint: = \pi , since it is the area of a semicircle of radius 1.)$ $\le$ 1 is revolved about the y-axis to generate a torus. Find its volume. (Hint: $Solve the problem. -The disk + \le 1 is revolved about the y-axis to generate a torus. Find its volume. (Hint: = \pi , since it is the area of a semicircle of radius 1.)$ = $Solve the problem. -The disk + \le 1 is revolved about the y-axis to generate a torus. Find its volume. (Hint: = \pi , since it is the area of a semicircle of radius 1.)$ $\pi$ , since it is the area of a semicircle of radius 1.)

(Multiple Choice)

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Question 69

Set up an integral for the length of the curve. -x = 6 tan y, 0 $\le$ y $\le$ $Set up an integral for the length of the curve. -x = 6 tan y, 0 \le y \le$

(Multiple Choice)

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Question 70

Find the area of the shaded region. -

(Multiple Choice)

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Question 71

Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by x = $Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by x = , 0 \le y \le , x = 0$ , 0 $\le$ y $\le$ $Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by x = , 0 \le y \le , x = 0$ , x = 0

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Question 72

Solve the problem. -A 20-m-long chain hangs vertically from a cylinder attached to a winch. Assume there is no friction in the system and that the chain has a density of 10 kg/m. How much work is required to wind the entire chain onto the cylinder using the winch?

(Multiple Choice)

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Question 73

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. -y = 9 , y = 9

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Question 74

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the y-axis

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Question 75

Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by x = 2tan , x = 0, y = -

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Question 76

Find the volume of the solid generated by revolving the region about the given axis. Use the shell or washer method. -The region in the first quadrant bounded by x = 5y - and the y-axis about the line x = -1

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Question 77

Solve the problem. -How much work is required to move an object from x = 0 to x = 6 (measured in meters) in the presence of a constant force of 10 N acting along the x-axis?

(Multiple Choice)

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Question 78

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = , y = 0, x = 0, x = 8

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Question 79

Find the area of the shaded region. -

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Question 80

Showing 61 - 80 of 211

Set up an integral for the length of the curve. -y = $Set up an integral for the length of the curve. -y = , 0 \le x \le 1$ , 0 $\le$ x $\le$ 1

Solve the problem. -A right circular cylinder is obtained by revolving the region enclosed by the line x = r, the x-axis, and the line about the y-axis. Find the volume of the cylinder.

Find the area enclosed by the given curves. -Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the line above left by y = x + 4, and above right by y = - + 10.

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the y-axis

Find the length of the curve. -y = ( - 2 ) from x = 1 to x = 8

A 1.5-mm layer of paint is applied to one side of the following surfaces. Find the volume of paint needed. Assume that x and y are measured in meters. -The spherical zone generated when the curve y = on the interval [ 4, 7] is revolved about the x-axis.

Set up an integral for the length of the curve. -x = 6 tan y, 0 $\le$ y $\le$ $Set up an integral for the length of the curve. -x = 6 tan y, 0 \le y \le$

Find the area of the shaded region. -

Solve the problem. -A 20-m-long chain hangs vertically from a cylinder attached to a winch. Assume there is no friction in the system and that the chain has a density of 10 kg/m. How much work is required to wind the entire chain onto the cylinder using the winch?

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. -y = 9 , y = 9

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the y-axis

Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by x = 2tan , x = 0, y = -

Find the volume of the solid generated by revolving the region about the given axis. Use the shell or washer method. -The region in the first quadrant bounded by x = 5y - and the y-axis about the line x = -1

Solve the problem. -How much work is required to move an object from x = 0 to x = 6 (measured in meters) in the presence of a constant force of 10 N acting along the x-axis?

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = , y = 0, x = 0, x = 8

Find the area of the shaded region. -

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Exam 6: Applications of Integration

Solve the problem. -A water tank is shaped like an inverted cone with height 18 m and base radius 3 m (see figure). If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank? Express the answer in terms of π\piπ .

Set up an integral for the length of the curve. -y = , 0 ≤\le≤ x ≤\le≤ 1

Solve the problem. -A right circular cylinder is obtained by revolving the region enclosed by the line x = r, the x-axis, and the line about the y-axis. Find the volume of the cylinder.

Find the area enclosed by the given curves. -Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the line above left by y = x + 4, and above right by y = - + 10.

Find the volume of the solid generated by revolving the shaded region about the given axis. -About the y-axis

Find the length of the curve. -y = ( - 2 ) from x = 1 to x = 8

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = , y = 0, 0 ≤\le≤ x ≤\le≤

A 1.5-mm layer of paint is applied to one side of the following surfaces. Find the volume of paint needed. Assume that x and y are measured in meters. -The spherical zone generated when the curve y = on the interval [ 4, 7] is revolved about the x-axis.

Solve the problem. -The disk + ≤\le≤ 1 is revolved about the y-axis to generate a torus. Find its volume. (Hint: = π\piπ , since it is the area of a semicircle of radius 1.)

Set up an integral for the length of the curve. -x = 6 tan y, 0 ≤\le≤ y ≤\le≤

Find the area of the shaded region. -

Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by x = , 0 ≤\le≤ y ≤\le≤ , x = 0

Solve the problem. -A 20-m-long chain hangs vertically from a cylinder attached to a winch. Assume there is no friction in the system and that the chain has a density of 10 kg/m. How much work is required to wind the entire chain onto the cylinder using the winch?

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis. -y = 9 , y = 9

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated axis. -About the y-axis

Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by x = 2tan , x = 0, y = -

Find the volume of the solid generated by revolving the region about the given axis. Use the shell or washer method. -The region in the first quadrant bounded by x = 5y - and the y-axis about the line x = -1

Solve the problem. -How much work is required to move an object from x = 0 to x = 6 (measured in meters) in the presence of a constant force of 10 N acting along the x-axis?

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = , y = 0, x = 0, x = 8

Find the area of the shaded region. -

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Set up an integral for the length of the curve. -y = $Set up an integral for the length of the curve. -y = , 0 \le x \le 1$ , 0 $\le$ x $\le$ 1

Set up an integral for the length of the curve. -x = 6 tan y, 0 $\le$ y $\le$ $Set up an integral for the length of the curve. -x = 6 tan y, 0 \le y \le$