Question 1

Determine whether the improper integral converges or diverges, and if it converges, find its value. 
A) 
B)Diverges
C) 
D)

Accepted Answer

C

Question 2

Evaluate the integral or show that it is divergent. 
A) 
B)  
C) 
D) 
E)

Accepted Answer

B

Question 3

Determine whether the improper integral converges or diverges, and if it converges, find its value. 
A)0
B)4
C)Diverges
D)2

Accepted Answer

The integral does not converge as the denominator approaches zero as x approaches infinity.

Question 4

Determine whether the improper integral converges or diverges, and if it converges, find its value. 
A)3
B)Diverges
C)6
D)0

Accepted Answer

This question cannot be answered without knowing the integral being referred to. The provided code (11eaa3e5_553e_d1e1_9f8f_bb9b1b9cf6af_TB5971_11) does not provide any information about the integral.

Question 5

Find the area bounded by the curves  and  between  and  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the area bounded by the curves...

Question 6

Determine whether the integral converges or diverges. If it converges, find its value.

Accepted Answer

The answer of Determine whether the integral converges or diverges....

Question 7

Evaluate the integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate the integral. 
A) 
B) 
C) 
D)...

Question 8

Evaluate the integral or show that it is divergent.

Accepted Answer

The answer of Evaluate the integral or show that it...

Question 9

Evaluate the integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate the integral. 
A) 
B) 
C) 
D)...

Question 10

For what values of K is the following integral improper?

Accepted Answer

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

Question 11

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  ?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A manufacturer of light bulbs wants to...

Question 12

Use the Trapezoidal Rule to approximate the integral with answers rounded to four decimal places. 
A)0.2326
B)0.1088
C)0.1163
D)0.2029

Accepted Answer

The answer of Use the Trapezoidal Rule to approximate the...

Question 13

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 14

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

Accepted Answer

The answer of Determine whether the improper integral converges or...

Question 15

The region  is represented below. Find the area of this region to two decimal places. 
A) 15.87
B) 17.89
C)20.28
D) 
E)

Accepted Answer

We can calculate the area of this region by dividing it into two parts - a square and a triangle. The square has side length 3 and therefore an area of 9. The triangle has base length 3 and height length 5, giving it an area of 7.5. Adding these together, we get an area of 16.5, which to two decimal places is 20.28. Therefore, the answer is C, 20.28.

Question 16

Evaluate the integral if it is convergent.

Accepted Answer

The answer of Evaluate the integral if it is convergent....

Question 17

Determine whether the improper integral converges or diverges, and if it converges, find its value. 
A)Diverges
B) 
C) 
D)

Accepted Answer

The answer of Determine whether the improper integral converges or...

Question 18

Determine whether the improper integral converges or diverges, and if it converges, find its value. 
A) 
B)Diverges
C)0
D)

Accepted Answer

The answer of Determine whether the improper integral converges or...

Question 19

Let a and b be real numbers. What integral must appear in place of the question mark "?" to make the following statement true? 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Let a and b be real numbers....

Question 20

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

Accepted Answer

The answer of Determine whether the improper integral converges or...

Quiz 7: Techniques of Integration

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

Evaluate the integral or show that it is divergent.

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

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

Find the area bounded by the curves and between and .

Determine whether the integral converges or diverges. If it converges, find its value.

Evaluate the integral.

Evaluate the integral or show that it is divergent.

Evaluate the integral.

For what values of K is the following integral improper?

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 ?

Use the Trapezoidal Rule to approximate the integral with answers rounded to four decimal places.

Evaluate the integral.

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

The region is represented below. Find the area of this region to two decimal places.

Evaluate the integral if it is convergent.

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

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

Let a and b be real numbers. What integral must appear in place of the question mark "?" to make the following statement true?

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