Find the area enclosed by the given curves. -y = x, y = x2

A) 1/12 B) 1/3 C) 1/6 D) 1/2 A) 1/12 B) 1/3 C) 1/6 D) 1/2

Exam 6: Applications of Integration

Determine the area of the surface generated when the curve is revolved about the indicated axis. -x = 3 $Determine the area of the surface generated when the curve is revolved about the indicated axis. -x = 3 , for 0 \le y \le ; about the y-axis$ , for 0 $\le$ y $\le$ $Determine the area of the surface generated when the curve is revolved about the indicated axis. -x = 3 , for 0 \le y \le ; about the y-axis$ ; about the y-axis

(Multiple Choice)

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Question 21

Find the volume of the described solid. -The solid lies between planes perpendicular to the x-axis at x = $\pi$ /6 to x = $\pi$ /2. The cross sections perpendicular to the x-axis are circular disks with diameters running from the curve $Find the volume of the described solid. -The solid lies between planes perpendicular to the x-axis at x = \pi /6 to x = \pi /2. The cross sections perpendicular to the x-axis are circular disks with diameters running from the curve to the curve$ to the curve $Find the volume of the described solid. -The solid lies between planes perpendicular to the x-axis at x = \pi /6 to x = \pi /2. The cross sections perpendicular to the x-axis are circular disks with diameters running from the curve to the curve$

(Multiple Choice)

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Question 22

Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by x = , x = 0, y = 1, y = 5

(Multiple Choice)

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Question 23

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the $Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = 5cos \pi x, y = 0, x = -0.5, x = 0.5$ -y = 5cos $\pi$ x, y = 0, x = -0.5, x = 0.5

(Multiple Choice)

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Question 24

Solve the problem. -Find a curve through the point ( -6, 1) whose length integral, 1 $\le$ y $\le$ 2, is L = $Solve the problem. -Find a curve through the point ( -6, 1) whose length integral, 1 \le y \le 2, is L =$

(Multiple Choice)

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Question 25

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

(Multiple Choice)

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Question 26

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

(Multiple Choice)

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Question 27

Solve the problem. -The lower edge of a dam is defined by the parabola (see figure). Use a coordinate system with y = 0 at the bottom of the dam to determine the total force on the dam. Lengths are measured in meters.

(Multiple Choice)

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Question 28

Find the area enclosed by the given curves. -Find the area between the curves y = ln x and y = ln 2x from x = 1 to x = 5.

(Multiple Choice)

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Question 29

Set up an integral for the length of the curve. -y = 8 cos x, 0 $\le$ x $\le$ $\pi$

(Multiple Choice)

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Question 30

Find the area of the shaded region. -

(Multiple Choice)

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Question 31

Find the area enclosed by the given curves. -Find the area of the region in the first quadrant bounded on the left by the line y = and on the right by the curves y = x and y = x. (Round to four decimal places.)

(Multiple Choice)

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Question 32

Find the area enclosed by the given curves. -y = x, y = x²

(Multiple Choice)

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Question 33

Solve the problem. -A diving pool that is 5 m deep and full of water has a viewing window on one of its vertical walls. Find the force on a circular window, with a radius of 0.5 m, tangent to the bottom of the pool. Round to three decimal places when appropriate.

(Multiple Choice)

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Question 34

Solve the problem. -A heavy-duty shock absorber is compressed 2 cm from its equilibrium position by a mass of 600 kg. How much work is required to compress the shock absorber 5 cm from its equilibrium position? (A mass of 600 kg exerts a force (in N) of 600g, where g $\approx$ 9.8 m/ $Solve the problem. -A heavy-duty shock absorber is compressed 2 cm from its equilibrium position by a mass of 600 kg. How much work is required to compress the shock absorber 5 cm from its equilibrium position? (A mass of 600 kg exerts a force (in N) of 600g, where g \approx 9.8 m/ .)$ .)

(Multiple Choice)

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Question 35

Solve the problem. -The hemispherical bowl of radius 5 contains water to a depth 2. Find the volume of water in the bowl.

(Multiple Choice)

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Question 36

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the $Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = 3cos ( \pi x), y = 3, x = -0.5, x = 0.5$ -y = 3cos ( $\pi$ x), y = 3, x = -0.5, x = 0.5

(Multiple Choice)

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Question 37

Find the volume of the solid generated by revolving the region about the given axis. Use the shell or washer method. -The region bounded by y = 7 , y = 7, and x = 0 about the y-axis

(Multiple Choice)

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Question 38

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines. -y = 4x, y = 0, x = 2; revolve about the line x = -3

(Multiple Choice)

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Question 39

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

(Multiple Choice)

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Question 40

Showing 21 - 40 of 211

Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by x = , x = 0, y = 1, y = 5

Solve the problem. -Find a curve through the point ( -6, 1) whose length integral, 1 $\le$ y $\le$ 2, is L = $Solve the problem. -Find a curve through the point ( -6, 1) whose length integral, 1 \le y \le 2, is L =$

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

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

Solve the problem. -The lower edge of a dam is defined by the parabola (see figure). Use a coordinate system with y = 0 at the bottom of the dam to determine the total force on the dam. Lengths are measured in meters.

Find the area enclosed by the given curves. -Find the area between the curves y = ln x and y = ln 2x from x = 1 to x = 5.

Set up an integral for the length of the curve. -y = 8 cos x, 0 $\le$ x $\le$ $\pi$

Find the area of the shaded region. -

Find the area enclosed by the given curves. -Find the area of the region in the first quadrant bounded on the left by the line y = and on the right by the curves y = x and y = x. (Round to four decimal places.)

Find the area enclosed by the given curves. -y = x, y = x²

Solve the problem. -A diving pool that is 5 m deep and full of water has a viewing window on one of its vertical walls. Find the force on a circular window, with a radius of 0.5 m, tangent to the bottom of the pool. Round to three decimal places when appropriate.

Solve the problem. -The hemispherical bowl of radius 5 contains water to a depth 2. Find the volume of water in the bowl.

Find the volume of the solid generated by revolving the region about the given axis. Use the shell or washer method. -The region bounded by y = 7 , y = 7, and x = 0 about the y-axis

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines. -y = 4x, y = 0, x = 2; revolve about the line x = -3

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

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Exam 6: Applications of Integration

Determine the area of the surface generated when the curve is revolved about the indicated axis. -x = 3 , for 0 ≤\le≤ y ≤\le≤ ; about the y-axis

Find the volume of the described solid. -The solid lies between planes perpendicular to the x-axis at x = π\piπ /6 to x = π\piπ /2. The cross sections perpendicular to the x-axis are circular disks with diameters running from the curve to the curve

Find the volume of the solid generated by revolving the region about the y-axis. -The region enclosed by x = , x = 0, y = 1, y = 5

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = 5cos π\piπ x, y = 0, x = -0.5, x = 0.5

Solve the problem. -Find a curve through the point ( -6, 1) whose length integral, 1 ≤\le≤ y ≤\le≤ 2, is L =

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

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

Solve the problem. -The lower edge of a dam is defined by the parabola (see figure). Use a coordinate system with y = 0 at the bottom of the dam to determine the total force on the dam. Lengths are measured in meters.

Find the area enclosed by the given curves. -Find the area between the curves y = ln x and y = ln 2x from x = 1 to x = 5.

Set up an integral for the length of the curve. -y = 8 cos x, 0 ≤\le≤ x ≤\le≤ π\piπ

Find the area of the shaded region. -

Find the area enclosed by the given curves. -Find the area of the region in the first quadrant bounded on the left by the line y = and on the right by the curves y = x and y = x. (Round to four decimal places.)

Find the area enclosed by the given curves. -y = x, y = x2

Solve the problem. -A diving pool that is 5 m deep and full of water has a viewing window on one of its vertical walls. Find the force on a circular window, with a radius of 0.5 m, tangent to the bottom of the pool. Round to three decimal places when appropriate.

Solve the problem. -A heavy-duty shock absorber is compressed 2 cm from its equilibrium position by a mass of 600 kg. How much work is required to compress the shock absorber 5 cm from its equilibrium position? (A mass of 600 kg exerts a force (in N) of 600g, where g ≈\approx≈ 9.8 m/ .)

Solve the problem. -The hemispherical bowl of radius 5 contains water to a depth 2. Find the volume of water in the bowl.

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the -y = 3cos ( π\piπ x), y = 3, x = -0.5, x = 0.5

Find the volume of the solid generated by revolving the region about the given axis. Use the shell or washer method. -The region bounded by y = 7 , y = 7, and x = 0 about the y-axis

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines. -y = 4x, y = 0, x = 2; revolve about the line x = -3

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

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

Solve the problem. -Find a curve through the point ( -6, 1) whose length integral, 1 $\le$ y $\le$ 2, is L = $Solve the problem. -Find a curve through the point ( -6, 1) whose length integral, 1 \le y \le 2, is L =$

Set up an integral for the length of the curve. -y = 8 cos x, 0 $\le$ x $\le$ $\pi$

Find the area enclosed by the given curves. -y = x, y = x²