Question 1

Find the area of the region under the curve   over the indicated interval. ​   ​

Accepted Answer

A)  2 sq units 
B)  3 sq units 
C)  4 sq units 
D)  8 sq units 
E)  1 sq units 
A)  2 sq units 
B)  3 sq units 
C)  4 sq units 
D)  8 sq units 
E)  1 sq units

Question 2

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. ​   ​

Accepted Answer

A)  By trapezoidal rule 1.2140, by Simpson's rule 1.1609 
B)  By trapezoidal rule 1.1705, by Simpson's rule 1.1520 
C)  By trapezoidal rule 1.1000, by Simpson's rule 1.1660 
D)  By trapezoidal rule 1.3620, by Simpson's rule 1.1306 
E)  By trapezoidal rule 0.9613, by Simpson's rule 0.9503 
A)  By trapezoidal rule 1.2140, by Simpson's rule 1.1609 
B)  By trapezoidal rule 1.1705, by Simpson's rule 1.1520 
C)  By trapezoidal rule 1.1000, by Simpson's rule 1.1660 
D)  By trapezoidal rule 1.3620, by Simpson's rule 1.1306 
E)  By trapezoidal rule 0.9613, by Simpson's rule 0.9503

Question 3

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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 $60/pair.
​

Accepted Answer

A)  ≈ $2,794 
B)  ≈ $3,131 
C)  ​≈ $3,223 
D)  ​≈ $2,054 
A)  ≈ $2,794 
B)  ≈ $3,131 
C)  ​≈ $3,223 
D)  ​≈ $2,054

Question 6

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. ​   ​

Accepted Answer

A)  By trapezoidal rule 1.1325, by Simpson's rule 0.6554 
B)  By trapezoidal rule 1.9565, by Simpson's rule 0.6555 
C)  By trapezoidal rule 0.6572, by Simpson's rule 0.6551 
D)  By trapezoidal rule 1.6290, by Simpson's rule 1.6108 
E)  By trapezoidal rule 1.5807, by Simpson's rule 0.6533 
A)  By trapezoidal rule 1.1325, by Simpson's rule 0.6554 
B)  By trapezoidal rule 1.9565, by Simpson's rule 0.6555 
C)  By trapezoidal rule 0.6572, by Simpson's rule 0.6551 
D)  By trapezoidal rule 1.6290, by Simpson's rule 1.6108 
E)  By trapezoidal rule 1.5807, by Simpson's rule 0.6533

Question 7

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 8

The commissioner of the City of Newton Department of Public Works estimates that the number of people in the city who have been recycling their magazines in year t following the introduction of the recycling program at the beginning of 1990 is
​   ​
Find the average number of people who will have recycled their magazines during the first 7 years since the program was introduced. Round to the nearest integer.
​
__________ people

Accepted Answer

The answer of The commissioner of the City of Newton...

Question 9

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 10

Approximate the value of the definite integral.
​   ​
Use the trapezoidal rule. Please give the answer to four decimal places.
​
Use the Simpson's rule. Please give the answer to four decimal places.
​
Find the exact value of the integral. Please give the answer to four decimal places.

Accepted Answer

0.1753; 0.

Question 11

Find the volume of the solid of revolution obtained by revolving the region bounded above by the curve
​   ​
and below by the curve
​   ​
from   to   about the   -axis.

Accepted Answer

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

Question 12

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Find the exact value of the integral. ​   ​

Accepted Answer

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

Question 13

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 14

Find the area of the region under the given curve   over the indicated interval.
​

Accepted Answer

The answer of Find the area of the region under...

Question 15

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

Accepted Answer

A)    
B)  ​   
C)  ​   
D)  ​   
E)  the integral is divergent 
A)    
B)  ​   
C)  ​   
D)  ​   
E)  the integral is divergent

Question 16

Find the indefinite integral.
​

Accepted Answer

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

Question 17

Find a bound on the error in approximating the definite integral using the trapezoidal rule with 8 intervals. ​   ​

Accepted Answer

A)  0.1773108 
B)  0.1110032 
C)  0.0629052 
D)  0.0625000 
E)  0.0403685 
A)  0.1773108 
B)  0.1110032 
C)  0.0629052 
D)  0.0625000 
E)  0.0403685

Question 18

Find a bound on the error in approximating the given definite integral using (a) the trapezoidal rule and (b) Simpson's rule with n intervals. ​   ​

Accepted Answer

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

Question 19

Find the volume of the solid of revolution obtained by revolving the region bounded above by the curve
​   ​
and below by the curve
​   ​
from   to   about the   -axis.

Accepted Answer

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

Question 20

In a study conducted by a certain country's Economic Development Board regarding the income distribution of certain segments of the country's workforce, it was found that the Lorentz curve for the distribution of income of college professors is described by the function ​   ​
Compute the coefficient of inequality of the Lorentz curve. Round to the nearest thousandth. Hint: Use the formula

Accepted Answer

A)  0.331 
B)  0.809 
C)  0.589 
D)  0.31 
A)  0.331 
B)  0.809 
C)  0.589 
D)  0.31

Find the area of the region under the curve over the indicated interval.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.

Find the indefinite integral.

Use the table of integrals to find the 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 $60/pair.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.

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

Find the indefinite integral.

Approximate the value of the definite integral. Use the trapezoidal rule. Please give the answer to four decimal places. Use the Simpson's rule. Please give the answer to four decimal places. Find the exact value of the integral. Please give the answer to four decimal places.

Find the volume of the solid of revolution obtained by revolving the region bounded above by the curve and below by the curve from to about the -axis.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Find the exact value of the integral.

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

Find the area of the region under the given curve over the indicated interval.

Evaluate the following improper integral whenever it is convergent.

Find the indefinite integral.

Find a bound on the error in approximating the definite integral using the trapezoidal rule with 8 intervals.

Find a bound on the error in approximating the given definite integral using (a) the trapezoidal rule and (b) Simpson's rule with n intervals.

Find the volume of the solid of revolution obtained by revolving the region bounded above by the curve and below by the curve from to about the -axis.

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 area of the region under the curve over the indicated interval. ​ ​

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. ​ ​

Find the indefinite integral. ​ ​

Use the table of integrals to find the 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 $60/pair. ​

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. ​ ​

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

Find the indefinite integral. ​ ​

Approximate the value of the definite integral. ​ ​ Use the trapezoidal rule. Please give the answer to four decimal places. ​ Use the Simpson's rule. Please give the answer to four decimal places. ​ Find the exact value of the integral. Please give the answer to four decimal places.

Find the volume of the solid of revolution obtained by revolving the region bounded above by the curve ​ ​ and below by the curve ​ ​ from to about the -axis.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Find the exact value of the integral. ​ ​

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

Find the area of the region under the given curve over the indicated interval. ​

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

Find the indefinite integral. ​

Find a bound on the error in approximating the definite integral using the trapezoidal rule with 8 intervals. ​ ​

Find a bound on the error in approximating the given definite integral using (a) the trapezoidal rule and (b) Simpson's rule with n intervals. ​ ​

Find the volume of the solid of revolution obtained by revolving the region bounded above by the curve ​ ​ and below by the curve ​ ​ from to about the -axis.

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 area of the region under the curve over the indicated interval.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.

Find the indefinite integral.

Use the table of integrals to find the 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 $60/pair.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.

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

Find the indefinite integral.

Approximate the value of the definite integral. Use the trapezoidal rule. Please give the answer to four decimal places. Use the Simpson's rule. Please give the answer to four decimal places. Find the exact value of the integral. Please give the answer to four decimal places.

Find the volume of the solid of revolution obtained by revolving the region bounded above by the curve and below by the curve from to about the -axis.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Find the exact value of the integral.

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

Find the area of the region under the given curve over the indicated interval.

Evaluate the following improper integral whenever it is convergent.

Find the indefinite integral.

Find a bound on the error in approximating the definite integral using the trapezoidal rule with 8 intervals.

Find a bound on the error in approximating the given definite integral using (a) the trapezoidal rule and (b) Simpson's rule with n intervals.

Find the volume of the solid of revolution obtained by revolving the region bounded above by the curve and below by the curve from to about the -axis.