Question 1

If the infinite curve   , is rotated about the x-axis , find the area of the resulting surface.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Find the centroid of the region bounded by the graphs of   and   .

Accepted Answer

The answer of Find the centroid of the region bounded...

Question 3

Find the area of the surface obtained by revolving the given curve about the x-axis.   on [0, 1]

Accepted Answer

The answer of Find the area of the surface obtained...

Question 4

Find the length of the line segment joining the two given points by finding the equation of the line using Equation (2). Then check your answer by using the distance formula. (0, 0), (1, 8)

Accepted Answer

A)    
B) 9 
C)    
D)    
A)    
B) 9 
C)    
D)

Question 5

For a given commodity and pure competition, the number of units produced and the price per unit are determined as the coordinates of the point of intersection of the supply and demand curves. Given the demand curve   and the supply curve   ,
find the consumer surplus.

Accepted Answer

The answer of For a given commodity and pure competition,...

Question 6

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)

Accepted Answer

A) 332.8 lb 
B) 1331.2 lb 
C) 2662.4 lb 
D) 665.6 lb 
A) 332.8 lb 
B) 1331.2 lb 
C) 2662.4 lb 
D) 665.6 lb

If the infinite curve , is rotated about the x-axis , find the area of the resulting surface.

Find the centroid of the region bounded by the graphs of and .

Find the area of the surface obtained by revolving the given curve about the x-axis. on [0, 1]

Find the length of the line segment joining the two given points by finding the equation of the line using Equation (2). Then check your answer by using the distance formula. (0, 0), (1, 8)

For a given commodity and pure competition, the number of units produced and the price per unit are determined as the coordinates of the point of intersection of the supply and demand curves. Given the demand curve and the supply curve , find the consumer surplus.

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft³.)

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Exam 8: Further Applications of Integration

If the infinite curve , is rotated about the x-axis , find the area of the resulting surface.

Find the centroid of the region bounded by the graphs of and .

Find the area of the surface obtained by revolving the given curve about the x-axis. on [0, 1]

Find the length of the line segment joining the two given points by finding the equation of the line using Equation (2). Then check your answer by using the distance formula. (0, 0), (1, 8)

For a given commodity and pure competition, the number of units produced and the price per unit are determined as the coordinates of the point of intersection of the supply and demand curves. Given the demand curve and the supply curve , find the consumer surplus.

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft³.)