Question 1

Find the partial fraction decomposition.

Accepted Answer

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

Question 2

Find an antiderivative.

Accepted Answer

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

Question 3

Find the partial fraction decomposition.

Accepted Answer

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

Question 4

The pdf describing the chance that a given insect will die at a particular age, x days, is   . What is the chance the insect will live longer than 10 days? Round your answer to three decimal places.

Accepted Answer

A)  0.594 
B)  0.100 
C)  0.406 
D)  0.500 
A)  0.594 
B)  0.100 
C)  0.406 
D)  0.500

Question 5

Find the indicated limit.

Accepted Answer

A)  0 
B)  1 
C)    
D)  limit does not exist 
A)  0 
B)  1 
C)    
D)  limit does not exist

Question 6

Evaluate the integral.

Accepted Answer

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

Question 7

Find the partial fraction decomposition.

Accepted Answer

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

Question 8

Evaluate the integral.

Accepted Answer

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

Question 9

Find the partial fraction decomposition.

Accepted Answer

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

Question 10

Evaluate the integral.

Accepted Answer

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

Question 11

Use a table of integrals to find an antiderivative.

Accepted Answer

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

Question 12

A given sample of a particular polymer will have molecules with a range of molecular weights, MW. If the molecular weight pdf is   , what fraction of the molecules will have a molecular weight greater than 1,000? Round your answer to four decimal places.

Accepted Answer

A)  0.3033 
B)  0.3935 
C)  10.0000 
D)  0.6065 
A)  0.3033 
B)  0.3935 
C)  10.0000 
D)  0.6065

Question 13

Evaluate the integral.

Accepted Answer

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

Question 14

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

Accepted Answer

A)  The integral diverges. 
B)  The integral evaluates to   . 
C)  The integral evaluates to   . 
D)  The integral evaluates to   . 
A)  The integral diverges. 
B)  The integral evaluates to   . 
C)  The integral evaluates to   . 
D)  The integral evaluates to   .

Question 15

Evaluate the integral.

Accepted Answer

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

Question 16

Find the partial fraction decomposition.

Accepted Answer

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

Question 17

Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer   ,   (Use integration by parts with   ).

Accepted Answer

The answer of Several useful integration formulas called reduction formulas...

Question 18

Evaluate the integral.

Accepted Answer

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

Question 19

Find the limit.

Accepted Answer

A)  0 
B)  1 
C)    
D)    
A)  0 
B)  1 
C)    
D)

Question 20

Evaluate the integral.

Accepted Answer

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

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find an antiderivative.

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

The pdf describing the chance that a given insect will die at a particular age, x days, is . What is the chance the insect will live longer than 10 days? Round your answer to three decimal places.

Find the indicated limit.

Evaluate the integral.

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Evaluate the integral.

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Evaluate the integral.

Use a table of integrals to find an antiderivative.

Evaluate the integral.

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

Evaluate the integral.

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer , (Use integration by parts with ).

Evaluate the integral.

Find the limit.

Evaluate the integral.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 8: Integration Techniques

Find the partial fraction decomposition.

Find an antiderivative.

Find the partial fraction decomposition.

The pdf describing the chance that a given insect will die at a particular age, x days, is . What is the chance the insect will live longer than 10 days? Round your answer to three decimal places.

Find the indicated limit.

Evaluate the integral.

Find the partial fraction decomposition.

Evaluate the integral.

Find the partial fraction decomposition.

Evaluate the integral.

Use a table of integrals to find an antiderivative.

A given sample of a particular polymer will have molecules with a range of molecular weights, MW. If the molecular weight pdf is , what fraction of the molecules will have a molecular weight greater than 1,000? Round your answer to four decimal places.

Evaluate the integral.

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

Evaluate the integral.

Find the partial fraction decomposition.

Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer , (Use integration by parts with ).

Evaluate the integral.

Find the limit.

Evaluate the integral.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the partial fraction decomposition. $Find the partial fraction decomposition.$