Question 1

Use integration tables to find   . ​

Accepted Answer

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

Question 2

Use a table of integrals with forms involving the trigonometric functions to find the integral.   ​

Accepted Answer

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

Question 3

Evaluate the definite integral   .

Accepted Answer

A)  3 
B)  6 
C)  4 
D)  0 
E)  7 
A)  3 
B)  6 
C)  4 
D)  0 
E)  7

Question 4

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 16 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral. ​   ​

Accepted Answer

A)  The Trapezoidal rule gives 1.4019 and Simpson's rule gives 1.4022. 
B)  The Trapezoidal rule gives 1.4010 and Simpson's rule gives 1.4720. 
C)  The Trapezoidal rule gives 1.4019 and Simpson's rule gives 1.4720. 
D)  The Trapezoidal rule gives 1.4010 and Simpson's rule gives 1.4022. 
E)  The Trapezoidal rule gives -1.4019 and Simpson's rule gives -1.4022. 
A)  The Trapezoidal rule gives 1.4019 and Simpson's rule gives 1.4022. 
B)  The Trapezoidal rule gives 1.4010 and Simpson's rule gives 1.4720. 
C)  The Trapezoidal rule gives 1.4019 and Simpson's rule gives 1.4720. 
D)  The Trapezoidal rule gives 1.4010 and Simpson's rule gives 1.4022. 
E)  The Trapezoidal rule gives -1.4019 and Simpson's rule gives -1.4022.

Question 5

Use integration tables to evaluate the integral   . ​

Accepted Answer

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

Question 6

Use partial fractions to find the integral   .

Accepted Answer

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

Question 7

Evaluate the definite integral   .

Accepted Answer

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B)    
C)    
D)    
E)    
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E)

Question 8

Suppose the capitalized cost C is given by   , where   is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and   is the annual cost of maintenance. Find the capitalized cost C of an asset forever if   . Round your answer to the nearest dollar. ​

Accepted Answer

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

Question 9

Find the indefinite integral.

Accepted Answer

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

Question 10

Use Simpson's Rule to approximate the value of the definite integral   with   . Round your answer to four decimal places. ​

Accepted Answer

A)  16.9283 
B)  22.3017 
C)  21.1805 
D)  24.5441 
E)  18.5139 
A)  16.9283 
B)  22.3017 
C)  21.1805 
D)  24.5441 
E)  18.5139

Question 11

Find the indefinite integral.

Accepted Answer

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

Question 12

Use integration tables to find   . ​

Accepted Answer

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

Question 13

Solve the differential equation   .

Accepted Answer

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

Question 14

Write the form of the partial fraction decomposition for the following rational expression.

Accepted Answer

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

Question 15

Use integration tables to find   . ​

Accepted Answer

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

Question 16

Use the Trapezoidal Rule to approximate the value of the definite integral   with   . Round your answer to four decimal places. ​

Accepted Answer

A)  18.2751 
B)  9.1375 
C)  4.5688 
D)  2.2844 
E)  1.1422 
A)  18.2751 
B)  9.1375 
C)  4.5688 
D)  2.2844 
E)  1.1422

Question 17

Find the indefinite integral by making the substitution   .

Accepted Answer

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

Question 18

Find the indefinite integral.

Accepted Answer

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

Question 19

Find the indefinite integral   .

Accepted Answer

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

Question 20

Find the indefinite integral.

Accepted Answer

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

Use integration tables to find .

Use a table of integrals with forms involving the trigonometric functions to find the integral.

Evaluate the definite integral .

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 16 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

Use integration tables to evaluate the integral .

Use partial fractions to find the integral $Use partial fractions to find the integral .$ .

Evaluate the definite integral .

Suppose the capitalized cost C is given by , where is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and is the annual cost of maintenance. Find the capitalized cost C of an asset forever if . Round your answer to the nearest dollar.

Find the indefinite integral.

Use Simpson's Rule to approximate the value of the definite integral with . Round your answer to four decimal places.

Find the indefinite integral.

Use integration tables to find .

Solve the differential equation .

Write the form of the partial fraction decomposition for the following rational expression. $Write the form of the partial fraction decomposition for the following rational expression.$

Use integration tables to find .

Use the Trapezoidal Rule to approximate the value of the definite integral with . Round your answer to four decimal places.

Find the indefinite integral by making the substitution .

Find the indefinite integral.

Find the indefinite integral .

Find the indefinite integral.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 8: Integration Techniques and Improper Integrals

Use integration tables to find . ​

Use a table of integrals with forms involving the trigonometric functions to find the integral. ​

Evaluate the definite integral .

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 16 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral. ​ ​

Use integration tables to evaluate the integral . ​

Use partial fractions to find the integral .

Evaluate the definite integral .

Suppose the capitalized cost C is given by , where is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and is the annual cost of maintenance. Find the capitalized cost C of an asset forever if . Round your answer to the nearest dollar. ​

Find the indefinite integral.

Use Simpson's Rule to approximate the value of the definite integral with . Round your answer to four decimal places. ​

Find the indefinite integral.

Use integration tables to find . ​

Solve the differential equation .

Write the form of the partial fraction decomposition for the following rational expression.

Use integration tables to find . ​

Use the Trapezoidal Rule to approximate the value of the definite integral with . Round your answer to four decimal places. ​

Find the indefinite integral by making the substitution .

Find the indefinite integral.

Find the indefinite integral .

Find the indefinite integral.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Use integration tables to find .

Use a table of integrals with forms involving the trigonometric functions to find the integral.

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 16 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

Use integration tables to evaluate the integral .

Use partial fractions to find the integral $Use partial fractions to find the integral .$ .

Suppose the capitalized cost C is given by , where is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and is the annual cost of maintenance. Find the capitalized cost C of an asset forever if . Round your answer to the nearest dollar.

Use Simpson's Rule to approximate the value of the definite integral with . Round your answer to four decimal places.

Use integration tables to find .

Write the form of the partial fraction decomposition for the following rational expression. $Write the form of the partial fraction decomposition for the following rational expression.$

Use integration tables to find .

Use the Trapezoidal Rule to approximate the value of the definite integral with . Round your answer to four decimal places.