Question 1

Evaluate the following improper integral whenever it is convergent. ​   ​

Accepted Answer

A)  -6 
B)  11 
C)  3 
D)  7 
E)  the integral is divergent 
A)  -6 
B)  11 
C)  3 
D)  7 
E)  the integral is divergent C

Question 2

The present value of a perpetual stream of income that flows continually at the rate of P(t) dollars per year is given by the formula ​   ​
Where r is the interest rate compounded continuously. Using this formula, find the present value of a perpetual net income stream that is generated at the rate of   dollars per year.
Hint:

Accepted Answer

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

Question 3

Find the indefinite integral. ​   ​Hint: First, make the substitution u= x+4 ; then, integrate by parts.

Accepted Answer

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

Question 4

Evaluate the following improper integral whenever it is convergent.
​   ​
Enter divergent if the integral is divergent.

Accepted Answer

The answer of Evaluate the following improper integral whenever it...

Question 5

Based on data collected during an experiment, a biologist found that the number of fruit flies (Drosophila) with a limited food supply could be approximated by the exponential model
​   ​
where t denotes the number of days since the beginning of the experiment. Find the average number of fruit flies in the colony in the first 12 days of the experiment and in the first 22 days. Please round your answers to the nearest integer.
​
The average number of fruit flies in the first 12 days : __________
​
The average number of fruit flies in the first 22 days : __________

Accepted Answer

The answer of Based on data collected during an experiment,...

Question 6

If f is a polynomial function of degree more than 3, then the approximation   using Simpson's rule is exact.

Accepted Answer

A) True 
 B)False

Question 7

Evaluate the following improper integral whenever it is convergent. ​   ​

Accepted Answer

A)  6 
B)  4 
C)  2 
D)  10 
E)  the integral is divergent 
A)  6 
B)  4 
C)  2 
D)  10 
E)  the integral is divergent

Question 8

Use the formula
​   ​
to find the integral.
​

Accepted Answer

The answer of Use the formula
​   ​
to find...

Question 9

Evaluate the definite integral by using the method of integration by parts. ​   ​

Accepted Answer

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

Question 10

Use the table of integrals to find the integral. ​   ​

Accepted Answer

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

Question 11

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 12

The present value of a perpetual stream of income that flows continually at the rate of P(t) dollars per year is given by the formula
​   ​
where r is the interest rate compounded continuously. Using this formula, find the present value of a perpetual net income stream that is generated at the rate of
​   ​
dollars per year.
​

Accepted Answer

The answer of The present value of a perpetual stream...

Question 13

In using the trapezoidal rule, the number of subintervals n must be even.

Accepted Answer

A) True 
 B)False

Question 14

In using Simpson's rule, the number of subintervals n may be chosen to be even.

Accepted Answer

A) True 
 B)False

Question 15

The demand function for Apex women's boots is
​   ​
where p is the wholesale unit price in dollars and x is the quantity demanded daily, in units of a hundred. Find the consumers' surplus if the wholesale price is set at $70/pair. Round the result to the nearest dollar.
​
$__________

Accepted Answer

The answer of The demand function for Apex women's boots...

Question 16

A manmade lake located in Lake View Condominiums has the shape depicted in the following figure. The measurements shown were taken at 10-foot intervals. Using Simpson's rule with   , estimate the surface area of the lake. Round the result to the nearest tenth.
​   ​
__________ ft2

Accepted Answer

Question 17

Use the formula ​   ​to find the integral.

Accepted Answer

The answer of Use the formula ​   ​to...

Question 18

If   exists, then   exists and   .

Accepted Answer

A) True 
 B)False

Question 19

A university alumni group wishes to provide an annual scholarship in the amount of $1,100 beginning next year. If the scholarship fund will earn an interest rate of 5% / year compounded continuously, find the amount of the endowment the alumni are required to make now. ​

Accepted Answer

A)  $22,559 
B)  $21,118 
C)  $22,000 
D)  $21,556 
A)  $22,559 
B)  $21,118 
C)  $22,000 
D)  $21,556

Question 20

Find the indefinite integral.
​

Accepted Answer

The answer of Find the indefinite integral.
​  ...

Evaluate the following improper integral whenever it is convergent.

Find the indefinite integral. Hint: First, make the substitution u= x+4 ; then, integrate by parts.

Evaluate the following improper integral whenever it is convergent. Enter divergent if the integral is divergent.

If f is a polynomial function of degree more than 3, then the approximation using Simpson's rule is exact.

Evaluate the following improper integral whenever it is convergent.

Use the formula to find the integral.

Evaluate the definite integral by using the method of integration by parts.

Use the table of integrals to find the integral.

Find the indefinite integral.

In using the trapezoidal rule, the number of subintervals n must be even.

In using Simpson's rule, the number of subintervals n may be chosen to be even.

The demand function for Apex women's boots is where p is the wholesale unit price in dollars and x is the quantity demanded daily, in units of a hundred. Find the consumers' surplus if the wholesale price is set at $70/pair. Round the result to the nearest dollar. $__________

A manmade lake located in Lake View Condominiums has the shape depicted in the following figure. The measurements shown were taken at 10-foot intervals. Using Simpson's rule with , estimate the surface area of the lake. Round the result to the nearest tenth. __________ ft²

Use the formula to find the integral.

If exists, then exists and .

A university alumni group wishes to provide an annual scholarship in the amount of $1,100 beginning next year. If the scholarship fund will earn an interest rate of 5% / year compounded continuously, find the amount of the endowment the alumni are required to make now.

Find the indefinite integral.

Preliminaries

Functions, Limits, and the Derivative

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Calculus of Several Variables

Differential Equations

Probability and Calculus

Taylor Polynomials and Infinite Series

Trigonometric Functions

Filters

Exam 7: Additional Topics in Integration

Evaluate the following improper integral whenever it is convergent. ​ ​

Find the indefinite integral. ​ ​Hint: First, make the substitution u= x+4 ; then, integrate by parts.

Evaluate the following improper integral whenever it is convergent. ​ ​ Enter divergent if the integral is divergent.

If f is a polynomial function of degree more than 3, then the approximation using Simpson's rule is exact.

Evaluate the following improper integral whenever it is convergent. ​ ​

Use the formula ​ ​ to find the integral. ​

Evaluate the definite integral by using the method of integration by parts. ​ ​

Use the table of integrals to find the integral. ​ ​

Find the indefinite integral. ​ ​

In using the trapezoidal rule, the number of subintervals n must be even.

In using Simpson's rule, the number of subintervals n may be chosen to be even.

The demand function for Apex women's boots is ​ ​ where p is the wholesale unit price in dollars and x is the quantity demanded daily, in units of a hundred. Find the consumers' surplus if the wholesale price is set at $70/pair. Round the result to the nearest dollar. ​ $__________

A manmade lake located in Lake View Condominiums has the shape depicted in the following figure. The measurements shown were taken at 10-foot intervals. Using Simpson's rule with , estimate the surface area of the lake. Round the result to the nearest tenth. ​ ​ __________ ft2

Use the formula ​ ​to find the integral.

If exists, then exists and .

A university alumni group wishes to provide an annual scholarship in the amount of $1,100 beginning next year. If the scholarship fund will earn an interest rate of 5% / year compounded continuously, find the amount of the endowment the alumni are required to make now. ​

Find the indefinite integral. ​

Preliminaries

Functions, Limits, and the Derivative

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Calculus of Several Variables

Differential Equations

Probability and Calculus

Taylor Polynomials and Infinite Series

Trigonometric Functions

Filters

Evaluate the following improper integral whenever it is convergent.

Find the indefinite integral. Hint: First, make the substitution u= x+4 ; then, integrate by parts.

Evaluate the following improper integral whenever it is convergent. Enter divergent if the integral is divergent.

Evaluate the following improper integral whenever it is convergent.

Use the formula to find the integral.

Evaluate the definite integral by using the method of integration by parts.

Use the table of integrals to find the integral.

Find the indefinite integral.

The demand function for Apex women's boots is where p is the wholesale unit price in dollars and x is the quantity demanded daily, in units of a hundred. Find the consumers' surplus if the wholesale price is set at $70/pair. Round the result to the nearest dollar. $__________

A manmade lake located in Lake View Condominiums has the shape depicted in the following figure. The measurements shown were taken at 10-foot intervals. Using Simpson's rule with , estimate the surface area of the lake. Round the result to the nearest tenth. __________ ft²

Use the formula to find the integral.

A university alumni group wishes to provide an annual scholarship in the amount of $1,100 beginning next year. If the scholarship fund will earn an interest rate of 5% / year compounded continuously, find the amount of the endowment the alumni are required to make now.

Find the indefinite integral.