In a movie stunt, a car is driven off a cliff and falls into the ocean 200 feet below. If the car is going 50 feet/second (horizontally) when it goes over the cliff, its horizontal position is described as x = 50 t, where t is the time in seconds. Its vertical position is described as y = 16 t2, where y is the distance below the cliff (i.e. y = 200 when the car hits the ocean). Compute the length of the path traversed by the falling car. Round to the nearest foot. [Hint: The two equations will need to be combined, eliminating t so that y is expressed as a function of x.]

A) 274 feet B) 279 feet C) 284 feet D) 289 feet A) 274 feet B) 279 feet C) 284 feet D) 289 feet

Exam 6: Applications of the Definite Integral

Two divers, one on the 15 ft platform and one on the 30 ft platform, hope to perform a joint dive in which they enter the water at the same time. If each begins with an upward jump with an initial velocity of at 14 ft/s, how much time difference should there be between the start of the two dives?

(Multiple Choice)

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Question 21

Find the volume of the solid formed by revolving the region bounded by about y = 0.

(Multiple Choice)

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Question 22

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by about x = 7.

(Multiple Choice)

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Question 23

Identify the graph and area of the region bounded by the curves . Use only one integral. The figures below are not necessarily to scale.

(Multiple Choice)

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Question 24

Approximate the length of the curve using 4 secant lines. Round to three decimal places. y = x⁴ 0 $\leq$ x $\leq$ 2

(Multiple Choice)

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Question 25

Find the area between the following curves on the given interval.

(Multiple Choice)

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Question 26

Show that the volume of a solid formed by revolving the region bounded by x = y² and x = r about x = r is .

(Essay)

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Question 27

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by about x = 5.

(Multiple Choice)

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Question 28

Identify the graph and the area bounded by the curves

(Multiple Choice)

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Question 29

What is the minimum speed a ball must be thrown upward if it is to reach a height of 13 feet?

(Multiple Choice)

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Question 30

In a movie stunt, a car is driven off a cliff and falls into the ocean 200 feet below. If the car is going 50 feet/second (horizontally) when it goes over the cliff, its horizontal position is described as x = 50 t, where t is the time in seconds. Its vertical position is described as y = 16 t², where y is the distance below the cliff (i.e. y = 200 when the car hits the ocean). Compute the length of the path traversed by the falling car. Round to the nearest foot. [Hint: The two equations will need to be combined, eliminating t so that y is expressed as a function of x.]

(Multiple Choice)

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Question 31

Let R be the region bounded by , the x-axis, and the y-axis. Compute the volume of the solid formed by revolving R about the x-axis.

(Multiple Choice)

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Question 32

A person 6' tall wants to buy a jump rope. If , when the rope is at its lowest point, his hands will be 2' apart and 3' above the ground, and if the rope will take on the shape of a parabola just barely hitting the ground, how long must the rope be? [Consider the form of the rope to be described by the equation , with the origin being a spot on the ground underneath the jumper.]

(Multiple Choice)

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Question 33

Let R be the region bounded by . Compute the volume of the solid formed by revolving R about y = 20.

(Multiple Choice)

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Question 34

A baseball pitcher releases the ball horizontally from a height of 5 ft with an initial speed of 120 ft/s. Find the height of the ball when it reaches home plate 60 feet away. Round to two decimal places. (Hint: Determine the time of flight from the x-equation, then use the y-equation to determine the height.)

(Multiple Choice)

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Question 35

Compute the volume of a solid formed by revolving the region bounded by

(Multiple Choice)

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Question 36

Identify the graph and area of the region bounded by the curves . Use only one integral. The figures below are not necessarily to scale.

(Multiple Choice)

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Question 37

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by about y = 10.

(Multiple Choice)

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Question 38

Let R be the region bounded by . Compute the volume of the solid formed by revolving R about x = 2.

(Multiple Choice)

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Question 39

Use Simpson's rule to estimate the volume from the given cross sectional areas. x(cm) -1)0 -0)5 0)0 0)5 1)0 A(x) (cm²) 1)4 1)5 2)0 2)5 2)6

(Multiple Choice)

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Question 40

Showing 21 - 40 of 85

Two divers, one on the 15 ft platform and one on the 30 ft platform, hope to perform a joint dive in which they enter the water at the same time. If each begins with an upward jump with an initial velocity of at 14 ft/s, how much time difference should there be between the start of the two dives?

Find the volume of the solid formed by revolving the region bounded by about y = 0.

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by about x = 7.

Identify the graph and area of the region bounded by the curves . Use only one integral. The figures below are not necessarily to scale.

Approximate the length of the curve using 4 secant lines. Round to three decimal places. y = x⁴ 0 $\leq$ x $\leq$ 2

Find the area between the following curves on the given interval.

Show that the volume of a solid formed by revolving the region bounded by x = y² and x = r about x = r is .

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by about x = 5.

Identify the graph and the area bounded by the curves

What is the minimum speed a ball must be thrown upward if it is to reach a height of 13 feet?

Let R be the region bounded by , the x-axis, and the y-axis. Compute the volume of the solid formed by revolving R about the x-axis.

Let R be the region bounded by . Compute the volume of the solid formed by revolving R about y = 20.

Compute the volume of a solid formed by revolving the region bounded by

Identify the graph and area of the region bounded by the curves . Use only one integral. The figures below are not necessarily to scale.

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by about y = 10.

Let R be the region bounded by . Compute the volume of the solid formed by revolving R about x = 2.

Use Simpson's rule to estimate the volume from the given cross sectional areas. x(cm) -1)0 -0)5 0)0 0)5 1)0 A(x) (cm²) 1)4 1)5 2)0 2)5 2)6

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 6: Applications of the Definite Integral

Two divers, one on the 15 ft platform and one on the 30 ft platform, hope to perform a joint dive in which they enter the water at the same time. If each begins with an upward jump with an initial velocity of at 14 ft/s, how much time difference should there be between the start of the two dives?

Find the volume of the solid formed by revolving the region bounded by about y = 0.

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by about x = 7.

Identify the graph and area of the region bounded by the curves . Use only one integral. The figures below are not necessarily to scale.

Approximate the length of the curve using 4 secant lines. Round to three decimal places. y = x4 0 ≤\leq≤ x ≤\leq≤ 2

Find the area between the following curves on the given interval.

Show that the volume of a solid formed by revolving the region bounded by x = y2 and x = r about x = r is .

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by about x = 5.

Identify the graph and the area bounded by the curves

What is the minimum speed a ball must be thrown upward if it is to reach a height of 13 feet?

Let R be the region bounded by , the x-axis, and the y-axis. Compute the volume of the solid formed by revolving R about the x-axis.

Let R be the region bounded by . Compute the volume of the solid formed by revolving R about y = 20.

Compute the volume of a solid formed by revolving the region bounded by

Identify the graph and area of the region bounded by the curves . Use only one integral. The figures below are not necessarily to scale.

Use cylindrical shells to compute the volume of the solid formed by revolving the region bounded by about y = 10.

Let R be the region bounded by . Compute the volume of the solid formed by revolving R about x = 2.

Use Simpson's rule to estimate the volume from the given cross sectional areas. x(cm) -1)0 -0)5 0)0 0)5 1)0 A(x) (cm2) 1)4 1)5 2)0 2)5 2)6

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Approximate the length of the curve using 4 secant lines. Round to three decimal places. y = x⁴ 0 $\leq$ x $\leq$ 2

Show that the volume of a solid formed by revolving the region bounded by x = y² and x = r about x = r is .

Use Simpson's rule to estimate the volume from the given cross sectional areas. x(cm) -1)0 -0)5 0)0 0)5 1)0 A(x) (cm²) 1)4 1)5 2)0 2)5 2)6