Question 1

Set up the definite integral that gives the area of the region bounded by the graph of   and   .

Accepted Answer

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

Question 2

If the accumulation function   is given by   , evaluate

Accepted Answer

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

Question 3

Find the area of the region bounded by the graphs of the algebraic functions.

Accepted Answer

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

Question 4

Concrete sections for the new building have the dimensions (in meters) and shape as shown in the figure (the picture is not necessarily drawn to scale). One cubic meter of concrete weighs 4320 pounds. Find the weight of the section. Round your answer to the nearest pound.

Accepted Answer

A)  268,492 pounds 
B)  263,654 pounds 
C)  216,267 pounds 
D)  242,187 pounds 
E)  251,865 pounds 
A)  268,492 pounds 
B)  263,654 pounds 
C)  216,267 pounds 
D)  242,187 pounds 
E)  251,865 pounds

Question 5

Find the area of the region bounded by the graphs of the algebraic functions.

Accepted Answer

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

Question 6

The surface of a machine part is the region between the graphs of   and   as shown in the figure. Find the area of the surface of the machine part. Round your answer to five decimal places.

Accepted Answer

A)  1.66667 
B)  0.41667 
C)  0.01333 
D)  33.33333 
E)  8.33333 
A)  1.66667 
B)  0.41667 
C)  0.01333 
D)  33.33333 
E)  8.33333

Question 7

Suppose that   and   model the revenue (in billions of dollars) for a large corporation. The model   gives projected annual revenues from 2008 through 2015, with   corresponding to 2008, and   gives projected revenues if there is a decrease in the rate of growth of corporate sales over the period. Approximate the total reduction in revenue if corporate sales are actually closer to the model   . Round your answer to three decimal places.

Accepted Answer

A)  $3.570 billion 
B)  $24.990 billion 
C)  $19.763 billion 
D)  $29.645 billion 
E)  $12.495 billion 
A)  $3.570 billion 
B)  $24.990 billion 
C)  $19.763 billion 
D)  $29.645 billion 
E)  $12.495 billion

Question 8

Find the area of the region bounded by the graphs of the algebraic functions.

Accepted Answer

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

Question 9

Find the area of the region bounded by the graphs of the function     . Round your answer to three decimal places.

Accepted Answer

A)  0.260 
B)  0.289 
C)  0.416 
D)  0.139 
E)  0.462 
A)  0.260 
B)  0.289 
C)  0.416 
D)  0.139 
E)  0.462

Question 10

Find the area of the region bounded by equations by integrating (i) with respect to x and (ii) with respect to y.

Accepted Answer

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

Question 11

Find the area of the region bounded by the graphs of the equations.   .

Accepted Answer

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

Question 12

Find the area of the region bounded by the graphs of the equations.

Accepted Answer

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

Question 13

Find the area of the region bounded by the graphs of the algebraic functions.

Accepted Answer

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

Question 14

Find the area of the region bounded by the equations by integrating (i) with respect to x and (ii) with respect to y.

Accepted Answer

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

Question 15

The integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral   .

Accepted Answer

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

Question 16

Concrete sections for the new building have the dimensions (in meters) and shape as shown in the figure (the picture is not necessarily drawn to scale). Find the area of the face of the section superimposed on the rectangular coordinate system. Round your answer to three decimal places.

Accepted Answer

A)  25.031   
B)  31.075   
C)  29.151   
D)  30.515   
E)  28.031   
A)  25.031   
B)  31.075   
C)  29.151   
D)  30.515   
E)  28.031

Question 17

The surface of a machine part is the region between the graphs of   and   as shown in the figure. Find k if the parabola is tangent to the graph of   . Round your answer to three decimal places.

Accepted Answer

A)  3.125 
B)  0.160 
C)  0.080 
D)  0.320 
E)  6.250 
A)  3.125 
B)  0.160 
C)  0.080 
D)  0.320 
E)  6.250

Question 18

The chief financial officer of a company reports that profits for the past fiscal year were $   million. The officer predicts that profits for the next 7 years will grow at a continuous annual rate somewhere between   % and 6%. Estimate the cumulative difference in total profit over the 7 years based on the predicted range of growth rates. Round your answer to three decimal places.

Accepted Answer

A)  $445.736 billion 
B)  $30.221 billion 
C)  $7.023 billion 
D)  $18.710 billion 
E)  $57.880 billion 
A)  $445.736 billion 
B)  $30.221 billion 
C)  $7.023 billion 
D)  $18.710 billion 
E)  $57.880 billion

Exam 7: Section 1: Applications of Integration

Set up the definite integral that gives the area of the region bounded by the graph of and .

If the accumulation function is given by , evaluate

Find the area of the region bounded by the graphs of the algebraic functions.

Concrete sections for the new building have the dimensions (in meters) and shape as shown in the figure (the picture is not necessarily drawn to scale). One cubic meter of concrete weighs 4320 pounds. Find the weight of the section. Round your answer to the nearest pound.

Find the area of the region bounded by the graphs of the algebraic functions.

The surface of a machine part is the region between the graphs of and as shown in the figure. Find the area of the surface of the machine part. Round your answer to five decimal places.

Find the area of the region bounded by the graphs of the algebraic functions.

Find the area of the region bounded by the graphs of the function . Round your answer to three decimal places.

Find the area of the region bounded by equations by integrating (i) with respect to x and (ii) with respect to y.

Find the area of the region bounded by the graphs of the equations. .

Find the area of the region bounded by the graphs of the equations.

Find the area of the region bounded by the graphs of the algebraic functions.

Find the area of the region bounded by the equations by integrating (i) with respect to x and (ii) with respect to y.

The integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral .

Concrete sections for the new building have the dimensions (in meters) and shape as shown in the figure (the picture is not necessarily drawn to scale). Find the area of the face of the section superimposed on the rectangular coordinate system. Round your answer to three decimal places.

The surface of a machine part is the region between the graphs of and as shown in the figure. Find k if the parabola is tangent to the graph of . Round your answer to three decimal places.

Section 1: Preparation for Calculus

Section 2: Preparation for Calculus

Section 3: Preparation for Calculus

Section 4: Preparation for Calculus

Section 5: Preparation for Calculus

Section 6: Preparation for Calculus

Section 1: Limits and Their Properties

Section 2: Limits and Their Properties

Section 3: Limits and Their Properties

Section 4: Limits and Their Properties

Section 5 : Limits and Their Properties

Section 1 : Differentiation

Section 2: Differentiation

Section 3: Differentiation

Section 4 : Differentiation

Section 5: Differentiation

Section 6: Differentiation

Section 7: Differentiation

Section 8: Differentiation

Section 1 : Applications of Differentiation

Section 2: Applications of Differentiation

Section 3: Applications of Differentiation

Section 4: Applications of Differentiation

Section 5: Applications of Differentiation

Section 6: Applications of Differentiation

Section 7: Applications of Differentiation

Section 8: Applications of Differentiation

Section 1: Integration

Section 2: Integration

Section 3: Integration

Section 4: Integration

Section 5: Integration

Section 6: Integration

Section 7: Integration

Section 8: Integration

Section 9: Integration

Section 1: Differential Equations

Section 2: Differential Equations

Section 3: Differential Equations

Section 4: Differential Equations

Section 5: Differential Equations

Section 2: Applications of Integration

Section 3: Applications of Integration

Section 4: Applications of Integration

Section 5: Applications of Integration

Section 6: Applications of Integration

Section 7: Applications of Integration

Section 1: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 2: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 3: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 4: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 5: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 6: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 7: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 8: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 1: Infinite Series

Section 2: Infinite Series

Section 3: Infinite Series

Section 4: Infinite Series

Section 5: Infinite Series

Section 6: Infinite Series

Section 7: Infinite Series

Section 8: Infinite Series