Question 1

Evaluate the improper integral if it is convergent.

Accepted Answer

A)  3 
B)  -3 
C)  2 
D)  4 
E)  divergent 
A)  3 
B)  -3 
C)  2 
D)  4 
E)  divergent C

Question 2

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

Accepted Answer

A)  0.0147433 
B)  0.1524687 
C)  0.1357261 
D)  0.1688325 
E)  0.0625000 
A)  0.0147433 
B)  0.1524687 
C)  0.1357261 
D)  0.1688325 
E)  0.0625000 E

Question 3

Accepted Answer

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

Question 4

The demand equation for the Sicard sports watch is given by   where x (measured in units of a thousand) is the quantity demanded per week and p is the unit price in dollars. Use Simpson's Rule and (take n = 8) to estimate the consumer's surplus if the market price is $25/watch.(Round your answer to two decimal places)

Accepted Answer

A)  $579,597.2 
B)  $364,597.2 
C)  $354,597.2 
D)  $344,597.2 
A)  $579,597.2 
B)  $364,597.2 
C)  $354,597.2 
D)  $344,597.2

Question 5

The demand equation for the Sicard sports watch is given by   where x (measured in units of a thousand) is the quantity demanded per week and p is the unit price in dollars. Use the Trapezoidal Rule (take n = 8) to estimate the consumers' surplus if the market price is $25/watch. Round answer to two decimal places.

Accepted Answer

A)  $392,373.56 
B)  $142.37 
C)  $142,373.56 
D)  $367,373.56 
A)  $392,373.56 
B)  $142.37 
C)  $142,373.56 
D)  $367,373.56

Question 6

Use the table of integrals to find the integral.   Hint: First use the substitution u = x + 6.
Use C as the constant of integration.

Accepted Answer

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

Question 7

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 8

The present value of a perpetual stream of income that flows continually at the rate of   dollars per year is given by the formula   where   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)

Question 9

Consumer spending in dollars per person on media and entertainment from 2004 through 2009 is given in the following table.   Use the Trapezoidal Rule with n = 5 to estimate the average yearly spending by consumers on media and entertainment over the period in question. Round answer to two decimal places.

Accepted Answer

A)  5124 
B)  854 
C)  1024.8 
D)  2376.6 
A)  5124 
B)  854 
C)  1024.8 
D)  2376.6

Question 10

The amount of time t (in seconds) it takes a motorist to react to a road emergency is a continuous random variable with probability density function   What is the expected reaction time for a motorist chosen at random?

Accepted Answer

A)  1.86 sec 
B)  1.88 sec 
C)  1.55 sec 
D)  1.5 sec 
A)  1.86 sec 
B)  1.88 sec 
C)  1.55 sec 
D)  1.5 sec

Question 11

Determine whether the statement is true or false.
In using Simpson's rule, the number of subintervals n may be chosen to be even.

Accepted Answer

The answer of Determine whether the statement is true or...

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

The revenue of Virtual Reality, a video-game arcade, is generated at the rate of   dollars. If the revenue is invested t years from now in a business earning interest at the rate of 13% / year compounded continuously, find the accumulated value of this stream of income at the end of 8 years . Round to the nearest dollar.

Accepted Answer

A)  $659,353 
B)  $655,251 
C)  $659,827 
D)  $658,680 
A)  $659,353 
B)  $655,251 
C)  $659,827 
D)  $658,680

Question 14

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 15

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

Accepted Answer

A)  10 sq units 
B)  12 sq units 
C)  9 sq units 
D)  6 sq units 
A)  10 sq units 
B)  12 sq units 
C)  9 sq units 
D)  6 sq units

Question 16

Find the expected value of the continuous random variable X associated with the probability density function over the indicated interval.

Accepted Answer

A)  1.49 
B)  1.3333 
C)  2.772 
D)  1.386 
A)  1.49 
B)  1.3333 
C)  2.772 
D)  1.386

Question 17

Find the indefinite integral.   Hint: Integrate by parts twice.

Accepted Answer

The answer of Find the indefinite integral.   Hint:...

Question 18

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

Accepted Answer

The answer of Evaluate the definite integral by using the...

Question 19

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 20

Accepted Answer

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

Evaluate the improper integral if it is convergent.

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

Use the table of integrals to find the integral. Hint: First use the substitution u = x + 6. Use C as the constant of integration.

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. $__________

The amount of time t (in seconds) it takes a motorist to react to a road emergency is a continuous random variable with probability density function What is the expected reaction time for a motorist chosen at random?

Determine whether the statement is true or false. In using Simpson's rule, the number of subintervals n may be chosen to be even.

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

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

Find the expected value of the continuous random variable X associated with the probability density function over the indicated interval.

Find the indefinite integral. Hint: Integrate by parts twice.

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

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

Preliminaries

Functions, Limits and the Derivative

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Calculus of Several Variables

Filters

Exam 7: Additional Topics in Integration

Evaluate the improper integral if it is convergent.

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

Use the table of integrals to find the integral. Hint: First use the substitution u = x + 6. Use C as the constant of integration.

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. $__________

The amount of time t (in seconds) it takes a motorist to react to a road emergency is a continuous random variable with probability density function What is the expected reaction time for a motorist chosen at random?

Determine whether the statement is true or false. In using Simpson's rule, the number of subintervals n may be chosen to be even.

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

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

Find the expected value of the continuous random variable X associated with the probability density function over the indicated interval.

Find the indefinite integral. Hint: Integrate by parts twice.

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

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

Preliminaries

Functions, Limits and the Derivative

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Calculus of Several Variables

Filters