Question 1

A manufacturer of light bulbs wants to produce bulbs that last about  hours but, of course, some bulbs burn out faster than others. Let  be the fraction of the company's bulbs that burn out before t hours.  lies between 0 and 1. Let  . What is the value of  ?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 2

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 3

The region under the graph of  on the interval [1, 2] is revolved about the x-axis. Find the volume of the resulting solid.

Accepted Answer

The answer of The region under the graph of ...

Question 4

Evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Determine whether the improper integral converges or diverges, and if it converges, find its value.

Accepted Answer

A)   
B) Diverges 
C) 0 
D)

Question 6

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 7

Evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Find the area of the region bounded by the hyperbola  and the line  .

Accepted Answer

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

Question 9

Find the integral.

Accepted Answer

A)   
B)   
C)   
D)

Question 10

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 11

Use the Table of Integrals to evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

For what values of K is the following integral improper?

Accepted Answer

The answer of For what values of K is the...

Question 13

Determine whether the improper integral converges or diverges, and if it converges, find its value.

Accepted Answer

A) 0 
B) 4 
C) Diverges 
D) 2

Question 14

Find the integral using an appropriate trigonometric substitution.

Accepted Answer

A)   
B)   
C)   
D)

Question 15

Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule with n subintervals.

Accepted Answer

The answer of Find a bound on the error in...

Question 16

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 17

Find the integral.

Accepted Answer

A)   
B)   
C)   
D)

Question 18

Use a table of integrals to evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)

Question 19

Find the integral.

Accepted Answer

A)   
B)   
C)   
D)

Question 20

Use a table of integrals to evaluate the integral.

Accepted Answer

A)   
B)   
C)   
D)

Exam 7: Techniques of Integration

A manufacturer of light bulbs wants to produce bulbs that last about hours but, of course, some bulbs burn out faster than others. Let be the fraction of the company's bulbs that burn out before t hours. lies between 0 and 1. Let . What is the value of ?

Evaluate the integral.

The region under the graph of on the interval [1, 2] is revolved about the x-axis. Find the volume of the resulting solid.

Evaluate the integral.

Determine whether the improper integral converges or diverges, and if it converges, find its value.

Evaluate the integral.

Evaluate the integral.

Find the area of the region bounded by the hyperbola and the line .

Find the integral.

Evaluate the integral.

Use the Table of Integrals to evaluate the integral.

For what values of K is the following integral improper?

Determine whether the improper integral converges or diverges, and if it converges, find its value.

Find the integral using an appropriate trigonometric substitution.

Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule with n subintervals.

Evaluate the integral.

Find the integral.

Use a table of integrals to evaluate the integral.

Find the integral.

Use a table of integrals to evaluate the integral.