Deck 6: Techniques of Integration

Question 1

Find the integral.

A)
B)
C)
D)

Answer 1

Question 2

Find the integral.

A)
B)
C)
D)

Answer 2

Question 3

Use a table of integrals to evaluate the integral.

A)
B)
C)
D)

Answer 3

Question 4

Use the Table of Integrals to evaluate the integral.

A)
B)
C)
D)
E)

Question 5

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

A)
B)
C) 15
D) Diverges

Question 6

Find the integral.

A)
B)
C)
D)

Question 7

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

A)
B) 0
C)
D) Diverges

Question 8

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

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

Question 9

Estimate the area of the shaded region by using the Trapezoidal Rule with n = 4.Round the answer to the nearest tenth.

Question 10

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) none of these

Question 11

Use the Table of Integrals to evaluate the integral.

Question 12

Evaluate the integral or show that it is divergent.

Question 13

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

A)
B)
C)
D)
E)

Question 14

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 15

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

A)
B)
C)
D)
E)

Question 16

A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let .What is the value of ?

A)
B)
C)
D)
E)

Question 17

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

Question 18

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

Question 19

Find the integral.

A)
B)
C)
D)

Question 20

Evaluate the integral.

Question 21

Find the integral.

A)
B)
C)
D)

Question 22

Find the integral using an appropriate trigonometric substitution.

A)
B)
C)
D)

Question 23

Evaluate the integral.

A)
B)
C)
D)

Question 24

Find the integral.

A)
B)
C)
D)

Question 25

Find the integral.

Question 26

Find the area of the region bounded by the hyperbola and the line x = 6.

Question 27

Evaluate the integral.

A)
B)
C)
D)
E)

Question 28

Evaluate the integral using the indicated trigonometric substitution.

Question 29

Find the integral.

Question 30

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

A)
B)
C)
D)
E)

Question 31

Evaluate the integral.

A)
B)
C)
D)
E) None of these

Question 32

Evaluate the integral using the indicated trigonometric substitution.

A)
B)
C)
D)
E)

Question 33

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

A)
B)
C)
D)
E) None of these

Question 34

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 35

Find the integral.

A)
B)
C)
D)

Question 36

Evaluate the indefinite integral.

A)
B)
C)
D)
E) None of these

Question 37

Find the integral.

A)
B)
C)
D)

Question 38

Find the integral using an appropriate trigonometric substitution.

A)
B)
C)
D)

Question 39

Evaluate the integral.

A)
B)
C)
D)
E) None of these

Question 40

Find the integral.

A)
B)
C)
D)

Question 41

Evaluate the integral.

Question 42

Evaluate the following integral

Question 43

Find the integral.

A)
B)
C)
D)