Question 1

Find the indefinite integral.
​

Accepted Answer

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

Question 2

Find the indefinite integral.
​

Accepted Answer

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

Question 3

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 4

Find the indefinite integral.
​   ​

Accepted Answer

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

Question 5

Use the formula
​   ​
to find the integral.
​

Accepted Answer

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

Question 6

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Compare your result with the exact value of the integral. Please give the answer to four decimal places.
​   ​
Trapezoidal rule:__________
​
Simpson's rule: __________
​
Exact value: __________

Accepted Answer

0.2879; 0.

Question 7

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 8

Find the volume of the solid of revolution obtained by revolving the region under the curve
​   ​
from   to   about the   -axis.

Accepted Answer

The answer of Find the volume of the solid of...

Question 9

Use the table of integrals to find the integral.
​   ​
Use C as the constant of integration.

Accepted Answer

The answer of Use the table of integrals to find...

Question 10

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 11

The amount of nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on a certain May day in a city has been approximated by ​   ​
Where A(t) is measured in pollutant standard index (PSI), and ​t is measured in hours, with t=0 corresponding to 4 A.M . Use the trapezoidal rule with n = 0 to estimate the average PSI between 4 A.M. and noon. Please round the answer to the nearest hundredth.
(Hint:  .) __________ nitrogen dioxides

Accepted Answer

The answer of The amount of nitrogen dioxide, a brown...

Question 12

Use the table of integrals to find the given integral.
​   ​
Use C as the constant of integration.

Accepted Answer

The answer of Use the table of integrals to find...

Question 13

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 14

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

Accepted Answer

A)    
B)    
C)  1 
D)  0 
E)  the integral is divergent 
A)    
B)    
C)  1 
D)  0 
E)  the integral is divergent

Question 15

Use the formula ​   ​
To find the integral.
​   ​

Accepted Answer

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

Question 16

Find the function f given that the slope of the tangent line to the graph of f at any point   and that the graph passes through the point (0, 3).

Accepted Answer

The answer of Find the function f given that the...

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

Use the table of integrals to find the integral.
​   ​
Use C as the constant of integration.

Accepted Answer

The answer of Use the table of integrals to find...

Question 19

A university alumni group wishes to provide an annual scholarship in the amount of $1,900 beginning next year. If the scholarship fund will earn an interest rate of 4% / year compounded continuously, find the amount of the endowment the alumni are required to make now.
​
$__________

Accepted Answer

The answer of A university alumni group wishes to provide...

Question 20

Find a bound on the error in approximating the definite integral
​   ​
Please round your answers to seven decimal places.
​
Using the trapezoidal rule with 8 intervals.
​
Using Simpson's rule with 8 intervals.

Accepted Answer

0.0078125;

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Use the formula to find the integral.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Compare your result with the exact value of the integral. Please give the answer to four decimal places. Trapezoidal rule: Simpson's rule: Exact value: __

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

Find the volume of the solid of revolution obtained by revolving the region under the curve from to about the -axis.

Use the table of integrals to find the integral. Use C as the constant of integration.

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

Use the table of integrals to find the given integral. Use C as the constant of integration.

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

Evaluate the following improper integral whenever it is convergent.

Use the formula To find the integral.

Find the function f given that the slope of the tangent line to the graph of f at any point and that the graph passes through the point (0, 3).

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

Use the table of integrals to find the integral. Use C as the constant of integration.

A university alumni group wishes to provide an annual scholarship in the amount of $1,900 beginning next year. If the scholarship fund will earn an interest rate of 4% / year compounded continuously, find the amount of the endowment the alumni are required to make now. $__________

Find a bound on the error in approximating the definite integral Please round your answers to seven decimal places. Using the trapezoidal rule with 8 intervals. Using Simpson's rule with 8 intervals.

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

Find the indefinite integral. ​

Find the indefinite integral. ​

Find the indefinite integral. ​ ​

Find the indefinite integral. ​ ​

Use the formula ​ ​ to find the integral. ​

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Compare your result with the exact value of the integral. Please give the answer to four decimal places. ​ ​ Trapezoidal rule:__________ ​ Simpson's rule: __________ ​ Exact value: __________

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

Find the volume of the solid of revolution obtained by revolving the region under the curve ​ ​ from to about the -axis.

Use the table of integrals to find the integral. ​ ​ Use C as the constant of integration.

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

Use the table of integrals to find the given integral. ​ ​ Use C as the constant of integration.

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

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

Use the formula ​ ​ To find the integral. ​ ​

Find the function f given that the slope of the tangent line to the graph of f at any point and that the graph passes through the point (0, 3).

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

Use the table of integrals to find the integral. ​ ​ Use C as the constant of integration.

A university alumni group wishes to provide an annual scholarship in the amount of $1,900 beginning next year. If the scholarship fund will earn an interest rate of 4% / year compounded continuously, find the amount of the endowment the alumni are required to make now. ​ $__________

Find a bound on the error in approximating the definite integral ​ ​ Please round your answers to seven decimal places. ​ Using the trapezoidal rule with 8 intervals. ​ Using Simpson's rule with 8 intervals.

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

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Find the indefinite integral.

Use the formula to find the integral.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Compare your result with the exact value of the integral. Please give the answer to four decimal places. Trapezoidal rule: Simpson's rule: Exact value: __

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

Find the volume of the solid of revolution obtained by revolving the region under the curve from to about the -axis.

Use the table of integrals to find the integral. Use C as the constant of integration.

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

Use the table of integrals to find the given integral. Use C as the constant of integration.

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

Evaluate the following improper integral whenever it is convergent.

Use the formula To find the integral.

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

Use the table of integrals to find the integral. Use C as the constant of integration.

A university alumni group wishes to provide an annual scholarship in the amount of $1,900 beginning next year. If the scholarship fund will earn an interest rate of 4% / year compounded continuously, find the amount of the endowment the alumni are required to make now. $__________

Find a bound on the error in approximating the definite integral Please round your answers to seven decimal places. Using the trapezoidal rule with 8 intervals. Using Simpson's rule with 8 intervals.