Question 1

Sketch the region enclosed by   Find the area of the region.

Accepted Answer

The answer of Sketch the region enclosed by  ...

Question 2

Sketch the region bounded by the graphs of the given equations and find the area of that region.

Accepted Answer

The answer of Sketch the region bounded by the graphs...

Question 3

Find the work done in pushing a car a distance of   while exerting a constant force of

Accepted Answer

The answer of Find the work done in pushing a...

Question 4

Select the correct Answer for each question.
-Find the area of the shaded region.

Accepted Answer

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

Question 5

Select the correct Answer for each question.
-Find the area of the region bounded by the given curves.

Accepted Answer

A) 2 
B)    
C) 4 
D)    
E)    
A) 2 
B)    
C) 4 
D)    
E)

Question 6

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line.Sketch the region and a representative rectangle.

Accepted Answer

The answer of Find the volume of the solid generated...

Question 7

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line.

Accepted Answer

The answer of Find the volume of the solid generated...

Question 8

A tank is full of water.Find the work required to pump the water out of the outlet.Select the correct Answer

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 9

Find the area of the region bounded by the given curves.

Accepted Answer

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

Question 10

Select the correct Answer for each question.
-Find the area of the region bounded by the given curves.

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 11

Select the correct Answer for each question.
-The height of a monument is   m.A horizontal cross-section at a distance x meters from the top is an equilateral triangle with side   meters.Find the volume of the monument.

Accepted Answer

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

Question 12

Find the average value of the function   on the interval

Accepted Answer

The answer of Find the average value of the function...

Question 13

Select the correct Answer for each question.
-Sketch a graph to estimate the x-coordinates of the points of intersection of the given curves.Then use this information to estimate the volume of the solid obtained by rotating about the y axis the region enclosed by these curves.Rounded to the nearest hundredth.

Accepted Answer

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

Question 14

Use cylindrical shells to find the volume of the solid.A sphere of radius   Select the correct Answer

Accepted Answer

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

Question 15

Select the correct Answer for each question.
-Find the volume of the solid that is obtained by revolving the region about the x-axis.

Accepted Answer

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

Question 16

Select the correct Answer for each question.
-Sketch the region bounded by the graphs of the given equations and find the area of their region.

Accepted Answer

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

Question 17

Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters).You discover that both napkin rings have the same height t as shown in the figure.Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius d through the center of a sphere of radius D and express theAnswer in terms of

Accepted Answer

The answer of Suppose you make napkin rings by drilling...

Question 18

Use the Midpoint Rule with   to approximate the area of the region bounded by the given curves.

Accepted Answer

The answer of Use the Midpoint Rule with  ...

Question 19

Find the area of the region bounded by the given curves (a) using integration with respect to   and (b) using integration with respect to

Accepted Answer

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

Question 20

Find the number(s)   such that the average value of the function   on the interval   is equal to

Accepted Answer

The answer of Find the number(s)   such that...

Sketch the region enclosed by Find the area of the region.

Sketch the region bounded by the graphs of the given equations and find the area of that region.

Find the work done in pushing a car a distance of while exerting a constant force of

Select the correct Answer for each question. -Find the area of the shaded region.

Select the correct Answer for each question. -Find the area of the region bounded by the given curves.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line.Sketch the region and a representative rectangle.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line.

A tank is full of water.Find the work required to pump the water out of the outlet.Select the correct Answer

Find the area of the region bounded by the given curves.

Select the correct Answer for each question. -Find the area of the region bounded by the given curves.

Select the correct Answer for each question. -The height of a monument is m.A horizontal cross-section at a distance x meters from the top is an equilateral triangle with side meters.Find the volume of the monument.

Find the average value of the function on the interval

Use cylindrical shells to find the volume of the solid.A sphere of radius Select the correct Answer

Select the correct Answer for each question. -Find the volume of the solid that is obtained by revolving the region about the x-axis.

Select the correct Answer for each question. -Sketch the region bounded by the graphs of the given equations and find the area of their region.

Use the Midpoint Rule with to approximate the area of the region bounded by the given curves.

Find the area of the region bounded by the given curves (a) using integration with respect to and (b) using integration with respect to

Find the number(s) such that the average value of the function on the interval is equal to

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Techniques of Integration

Further Applications 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

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Exam 6: Applications of Integration

Sketch the region enclosed by Find the area of the region.

Sketch the region bounded by the graphs of the given equations and find the area of that region.

Find the work done in pushing a car a distance of while exerting a constant force of

Select the correct Answer for each question. -Find the area of the shaded region.

Select the correct Answer for each question. -Find the area of the region bounded by the given curves.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line.Sketch the region and a representative rectangle.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line.

A tank is full of water.Find the work required to pump the water out of the outlet.Select the correct Answer

Find the area of the region bounded by the given curves.

Select the correct Answer for each question. -Find the area of the region bounded by the given curves.

Select the correct Answer for each question. -The height of a monument is m.A horizontal cross-section at a distance x meters from the top is an equilateral triangle with side meters.Find the volume of the monument.

Find the average value of the function on the interval

Use cylindrical shells to find the volume of the solid.A sphere of radius Select the correct Answer

Select the correct Answer for each question. -Find the volume of the solid that is obtained by revolving the region about the x-axis.

Select the correct Answer for each question. -Sketch the region bounded by the graphs of the given equations and find the area of their region.

Use the Midpoint Rule with to approximate the area of the region bounded by the given curves.

Find the area of the region bounded by the given curves (a) using integration with respect to and (b) using integration with respect to

Find the number(s) such that the average value of the function on the interval is equal to

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Techniques of Integration

Further Applications 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

Filters