Deck 6: Techniques of Integration

Question 1

Use the Table of Integrals to evaluate the integral to three decimal places.

Answer 1

Question 2

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)

Answer 2

Question 3

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

A)
B)
C)Diverges
D)

Answer 3

Question 4

Find the integral.

A)
B)
C)
D)

Question 5

Evaluate the integral or show that it is divergent.

Question 6

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

A)0
B)Diverges
C)6
D)3

Question 7

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)

Question 8

Evaluate the integral.

Question 9

Find the integral.

A)
B)
C)
D)

Question 10

Use Simpson's Rule to approximate the integral with answers rounded to four decimal places.

A)3.6993
B)2.9599
C)4.0689
D)3.3296

Question 11

Use Simpson's Rule to approximate the integral with answers rounded to four decimal places.

A)2.0076
B)2.6098
C)2.9504
D)2.2955

Question 12

Use the Table of Integrals to evaluate the integral.

Question 13

Use the Midpoint Rule to approximate the given integral with the specified value of . (Round your answers to four decimal places.)

A)
B)
C)
D)
E)

Question 14

Estimate the area of the shaded region by using the Trapezoidal Rule with . Round the answer to the nearest tenth.

Question 15

Write the form of the partial fraction decomposition of the rational expression. Do not find the numerical values of the constants.

A)
B)
C)
D)

Question 16

Use the Midpoint Rule to approximate the given integral with the specified value of . (Round your answers to four decimal places.)

A)
B)
C)
D)
E)

Question 17

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

A)0
B)Diverges
C)
D)

Question 18

Use a table of integrals to evaluate the integral.

A)
B)
C)
D)

Question 19

Find the integral.

A)
B)
C)
D)

Question 20

Use the Table of Integrals to evaluate the integral.

A)
B)
C)
D)
E)

Question 21

Find the integral.

Question 22

Find the integral.

A)
B)
C)
D)

Question 23

Make a substitution to express the integrand as a rational function and then evaluate the integral. Round the answer to four decimal places.

Question 24

Find the integral using an appropriate trigonometric substitution.

A)
B)
C)
D)

Question 25

Find the integral.

A)
B)
C)
D)

Question 26

Evaluate the integral.

A)
B)
C)
D)

Question 27

Find the integral.

A)
B)
C)
D)

Question 28

Household electricity is supplied in the form of alternating current that varies from 170 V to -170 V with a frequency of 60 cycles per second (Hz). The voltage is thus given by the function E(t), where t is the time in seconds. Voltmeters read the RMS (root-mean-square) voltage, which is the square root of the average value of over one cycle. Calculate the RMS voltage of household current. Round your answer to the nearest integer.

Question 29

Evaluate the integral.

A)
B)
C)
D)
E)

Question 30

A particle moves on a straight line with velocity function $\Omega$ . Find its position function .

A)
B)
C)
D)
E)

Question 31

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

Question 32

Evaluate the integral using the indicated trigonometric substitution.

Question 33

Find the integral.

A)
B)
C)
D)

Question 34

Evaluate the indefinite integral.

A)
B)
C)
D)
E)

Question 35

Find the integral.

A)
B)
C)
D)

Question 36

Find the integral using an appropriate trigonometric substitution.

A)
B)
C)
D)

Question 37

Find the integral.

Question 38

Evaluate the integral using the indicated trigonometric substitution.

A)
B)
C)
D)
E)

Question 39

Find the integral.

A)
B)
C)
D)

Question 40

Evaluate the integral using integration by parts with the indicated choices of u and dv.

A)
B)
C)
D)
E)

Question 41

Evaluate the integral.

A)6.5700
B)
C)
D)0.7166
E)11.8665

Question 42

Evaluate the following integral.

Question 43

Find the integral.

A)
B)
C)
D)

Question 44

Evaluate the integral.

A)
B)
C)
D)
E)

Question 45

Evaluate the integral.

A)
B)
C)
D)
E)

Question 46

Evaluate the integral.