Question 1

Find the average value of the function ​   ​
Over the indicated interval   .
​

Accepted Answer

A)  2 
B)    
C)  0 
A)  2 
B)    
C)  0 B

Question 2

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ​
If f and g are integrable, then   .
​

Accepted Answer

A)  False. The indefinite integral of a difference of two integrable functions is not equal to the difference of their indefinite integrals. The indefinite integral of a constant multiple of a function is equal to the constant multiple of the indefinite integral of the function. 
B)  True. The indefinite integral of a difference of two integrable functions is equal to the difference of their indefinite integrals. The indefinite integral of a constant multiple of a function is equal to the constant multiple of the indefinite integral of the function. 
A)  False. The indefinite integral of a difference of two integrable functions is not equal to the difference of their indefinite integrals. The indefinite integral of a constant multiple of a function is equal to the constant multiple of the indefinite integral of the function. 
B)  True. The indefinite integral of a difference of two integrable functions is equal to the difference of their indefinite integrals. The indefinite integral of a constant multiple of a function is equal to the constant multiple of the indefinite integral of the function. B

Question 3

Find the indefinite integral.
​

Accepted Answer

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

Question 4

Evaluate the definite integral.
​

Accepted Answer

The answer of Evaluate the definite integral.
​  ...

Question 5

Estimate the present value of an annuity if payments are $700 monthly for 14 years and the account earns interest at the rate of 4% /year compounded continuously. Round your answer to the nearest dollar. ​

Accepted Answer

A)  $85,725 
B)  $90,046 
C)  $91,280 
D)  $92,189 
A)  $85,725 
B)  $90,046 
C)  $91,280 
D)  $92,189

Question 6

Find the average value of the function
​   ​
over the indicated interval   .

Accepted Answer

The answer of Find the average value of the function
​...

Question 7

Find the area of the shaded region.
​
​

Accepted Answer

The answer of Find the area of the shaded region.
​
​...

Question 8

Find the area of the shaded region.
​
​

Accepted Answer

The answer of Find the area of the shaded region.
​
​...

Question 9

Find the area of the region under the graph of the function   on the interval   . ​   ;   ​

Accepted Answer

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

Question 10

Find the average value of the function ​   ​
Over the indicated interval   .
​

Accepted Answer

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

Question 11

Find the area of the region under the graph of the function ​   ​
On the interval   .
​

Accepted Answer

A)    sq units 
B)    sq units 
C)    sq units 
D)    sq units 
A)    sq units 
B)    sq units 
C)    sq units 
D)    sq units

Question 12

Lorimar Watch Company manufactures travel clocks. The daily marginal cost function associated with producing these clocks is
​   ​
where   is measured in dollars/unit and x denotes the number of units produced. Management has determined that the daily fixed cost incurred in producing these clocks is $130. Find the total cost incurred by Lorimar in producing the first 500 travel clocks/day.
​
$__________

Accepted Answer

The answer of Lorimar Watch Company manufactures travel clocks. The...

Question 13

Let   and compute the Riemann sum of f over the interval   , using ​
Two subintervals of equal length (   ).
​
Five subintervals of equal length (   ).
​
Ten subintervals of equal length (   ).
​
In each case, choose the representative points to be the right end points of the subintervals. Round your answer to two decimal places.
​

Accepted Answer

A)  213.75 sq units; 182.47 sq units; 190.08 sq units; 
B)  213.75 sq units; 190.08 sq units; 182.47 sq units; 
C)  182.47 sq units; 190.08 sq units; 213.75 sq units; 
D)  190.08 sq units; 182.47 sq units; 213.75 sq units; 
A)  213.75 sq units; 182.47 sq units; 190.08 sq units; 
B)  213.75 sq units; 190.08 sq units; 182.47 sq units; 
C)  182.47 sq units; 190.08 sq units; 213.75 sq units; 
D)  190.08 sq units; 182.47 sq units; 213.75 sq units;

Question 14

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 15

Find the indefinite integral.
​

Accepted Answer

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

Question 16

Find the average value of the function ​   ​
Over the indicated interval   .
​

Accepted Answer

A)  12 
B)  11 
C)  13 
D)  16 
A)  12 
B)  11 
C)  13 
D)  16

Question 17

Based on a preliminary report by a geological survey team, it is estimated that a newly discovered oil field can be expected to produce oil at the rate of ​   ​
Thousand barrels/year, t years after production begins. Find the amount of oil that the field can be expected to yield during the first 17 years of production, assuming that the projection holds true.
​

Accepted Answer

A)  1,086 thousand barrels 
B)  1,093 thousand barrels 
C)  1,090 thousand barrels 
D)  1,098 thousand barrels 
A)  1,086 thousand barrels 
B)  1,093 thousand barrels 
C)  1,090 thousand barrels 
D)  1,098 thousand barrels

Question 18

It is known that the quantity demanded of a certain make of portable hair dryer is x hundred units/week and the corresponding wholesale unit price is
​   ​
dollars. Determine the consumers' surplus if the wholesale market price is set at $10/unit. Round your answer to the nearest dollar.
​
$__________

Accepted Answer

The answer of It is known that the quantity demanded...

Question 19

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 20

Evaluate the definite integral. ​   ​

Accepted Answer

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

Find the average value of the function Over the indicated interval .

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If f and g are integrable, then .

Find the indefinite integral.

Evaluate the definite integral.

Estimate the present value of an annuity if payments are $700 monthly for 14 years and the account earns interest at the rate of 4% /year compounded continuously. Round your answer to the nearest dollar.

Find the average value of the function over the indicated interval .

Find the area of the shaded region.

Find the area of the shaded region.

Find the area of the region under the graph of the function on the interval . ;

Find the average value of the function Over the indicated interval .

Find the area of the region under the graph of the function On the interval .

Find the indefinite integral.

Find the indefinite integral.

Find the average value of the function Over the indicated interval .

It is known that the quantity demanded of a certain make of portable hair dryer is x hundred units/week and the corresponding wholesale unit price is dollars. Determine the consumers' surplus if the wholesale market price is set at $10/unit. Round your answer to the nearest dollar. $__________

Find the indefinite integral.

Evaluate the definite integral.

Preliminaries

Functions, Limits, and the Derivative

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Probability and Calculus

Taylor Polynomials and Infinite Series

Trigonometric Functions

Filters

Exam 6: Integration

Find the average value of the function ​ ​ Over the indicated interval . ​

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ​ If f and g are integrable, then . ​

Find the indefinite integral. ​

Evaluate the definite integral. ​

Estimate the present value of an annuity if payments are $700 monthly for 14 years and the account earns interest at the rate of 4% /year compounded continuously. Round your answer to the nearest dollar. ​

Find the average value of the function ​ ​ over the indicated interval .

Find the area of the shaded region. ​ ​

Find the area of the shaded region. ​ ​

Find the area of the region under the graph of the function on the interval . ​ ; ​

Find the average value of the function ​ ​ Over the indicated interval . ​

Find the area of the region under the graph of the function ​ ​ On the interval . ​

Find the indefinite integral. ​ ​

Find the indefinite integral. ​

Find the average value of the function ​ ​ Over the indicated interval . ​

Find the indefinite integral. ​ ​

Evaluate the definite integral. ​ ​

Preliminaries

Functions, Limits, and the Derivative

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Probability and Calculus

Taylor Polynomials and Infinite Series

Trigonometric Functions

Filters

Find the average value of the function Over the indicated interval .

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If f and g are integrable, then .

Find the indefinite integral.

Evaluate the definite integral.

Estimate the present value of an annuity if payments are $700 monthly for 14 years and the account earns interest at the rate of 4% /year compounded continuously. Round your answer to the nearest dollar.

Find the average value of the function over the indicated interval .

Find the area of the shaded region.

Find the area of the shaded region.

Find the area of the region under the graph of the function on the interval . ;

Find the average value of the function Over the indicated interval .

Find the area of the region under the graph of the function On the interval .

Find the indefinite integral.

Find the indefinite integral.

Find the average value of the function Over the indicated interval .

Find the indefinite integral.

Evaluate the definite integral.