Question 1

Use integration tables to evaluate the integral   . ​

Accepted Answer

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

Question 2

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 10 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 13.7000 and Simpson's rule gives 14.3588. 
B)  The Trapezoidal rule gives 13.7000 and Simpson's rule gives 13.6667. 
C)  The Trapezoidal rule gives -13.6750 and Simpson's rule gives -13.6667. 
D)  The Trapezoidal rule gives 13.6750 and Simpson's rule gives 13.6667. 
E)  The Trapezoidal rule gives 13.6750 and Simpson's rule gives 14.3588. 
A)  The Trapezoidal rule gives 13.7000 and Simpson's rule gives 14.3588. 
B)  The Trapezoidal rule gives 13.7000 and Simpson's rule gives 13.6667. 
C)  The Trapezoidal rule gives -13.6750 and Simpson's rule gives -13.6667. 
D)  The Trapezoidal rule gives 13.6750 and Simpson's rule gives 13.6667. 
E)  The Trapezoidal rule gives 13.6750 and Simpson's rule gives 14.3588. D

Question 3

Find the indefinite integral.

Accepted Answer

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

Question 4

A population is growing according to the logistic model   , where t is the time in days. Find the average population over the interval   . Round your answer to one decimal place. ​

Accepted Answer

A)    ft. lbs 
B)    ft. lbs 
C)    ft. lbs 
D)    ft. lbs 
E)    ft. lbs 
A)    ft. lbs 
B)    ft. lbs 
C)    ft. lbs 
D)    ft. lbs 
E)    ft. lbs

Question 5

Find the indefinite integral.

Accepted Answer

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

Question 6

Use integration tables to find   . ​

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Find the integral using integration by parts.   ​

Accepted Answer

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

Question 9

Find the indefinite integral.

Accepted Answer

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

Question 10

Use integration tables to find the integral   . ​

Accepted Answer

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

Question 11

Determine whether the improper integral   diverges or converges. Evaluate the integral if it converges.

Accepted Answer

A)    
B)    
A)    
B)

Question 12

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

Accepted Answer

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

Question 13

Use substitution to find the integral   .

Accepted Answer

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

Question 14

Complete the square and find   .

Accepted Answer

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

Question 15

Evaluate   . Round your answer to three decimal places.

Accepted Answer

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

Question 16

Use a table of integrals to find the integral.   ​

Accepted Answer

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

Question 17

Find the indefinite integral.

Accepted Answer

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

Question 18

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

Accepted Answer

A)  -2.1765 
B)  -2.4111 
C)  -8.0188 
D)  -10.6918 
E)  -2.6729 
A)  -2.1765 
B)  -2.4111 
C)  -8.0188 
D)  -10.6918 
E)  -2.6729

Question 19

Find the indefinite integral.

Accepted Answer

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

Question 20

Find the definite integral.

Accepted Answer

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

Use integration tables to evaluate the integral .

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 10 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

Find the indefinite integral.

A population is growing according to the logistic model , where t is the time in days. Find the average population over the interval . Round your answer to one decimal place.

Find the indefinite integral.

Use integration tables to find .

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

Find the integral using integration by parts.

Find the indefinite integral.

Use integration tables to find the integral .

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

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 substitution to find the integral .

Complete the square and find .

Evaluate . Round your answer to three decimal places.

Use a table of integrals to find the integral.

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.

Find the definite 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 evaluate the integral . ​

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 10 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral. ​ ​

Find the indefinite integral.

A population is growing according to the logistic model , where t is the time in days. Find the average population over the interval . Round your answer to one decimal place. ​

Find the indefinite integral.

Use integration tables to find . ​

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

Find the integral using integration by parts. ​

Find the indefinite integral.

Use integration tables to find the integral . ​

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

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

Use substitution to find the integral .

Complete the square and find .

Evaluate . Round your answer to three decimal places.

Use a table of integrals to find the integral. ​

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.

Find the definite 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 evaluate the integral .

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 10 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.

A population is growing according to the logistic model , where t is the time in days. Find the average population over the interval . Round your answer to one decimal place.

Use integration tables to find .

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

Find the integral using integration by parts.

Use integration tables to find the integral .

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 a table of integrals to find the integral.

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