Deck 8: Integration Techniques

Question 1

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) + C
B) - + C
C) - + C
D) + C

Answer 1

- + C

Question 2

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) -6 sin + C
B) - cos + C
C) 6 cos + C
D) sin + C

Answer 2

sin + C

Question 3

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) 7
B) 2
C) 8
D) 11

Answer 3

8

Question 4

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) + C
B)- + C
C) + C
D) - + C

Question 5

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) ln + C
B) ln + C
C) 4 ln + C
D) ln + C

Question 6

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) + C
B) 2 + C
C) + C
D) 2 + C

Question 7

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A)
B)
C)
D)

Question 8

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) 1
B) 144
C) 2304
D) 144

Question 9

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A)
B)
C)
D)

Question 10

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A)
B)
C)
D)

Question 11

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A)
B)
C)
D)

Question 12

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-dx

A) x + 8 ln + C
B) x - 8 ln + C
C) x - 8 ln + C
D) x + 8 ln + C

Question 13

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A)
B)
C)
D)

Question 14

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A)
B)
C)
D)

Question 15

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A)
B)
C)
D)

Question 16

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A)
B)
C)
D)

Question 17

Choose the one alternative that best completes the statement or answers the question. Evaluate the integral

-

A) tan $\theta$ + sec $\theta$
B) $\theta$ - tan $\theta$
C) tan $\theta$ - sec $\theta$
D) $\theta$ + sec $\theta$

Question 18

Solve the problem.

-Find the area of the entire region bounded by the curves and

A) 1
B) - 6 ln 12
C) 0
D) 9 - 12 ln 12

Question 19

Solve the problem.

-Consider the region R bounded by the graph of f(x) = on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the x-axis.

A) + 15
B)
C)
D)

Question 20

Solve the problem.

-Consider the region R bounded by the graph of f(x) = on the interval [0, 3]. Find the volume of the solid formed when R is revolved about the y-axis.

A) $\pi$
B) 2 $\pi$
C) $\pi$
D) 2 $\pi$

Question 21

Evaluate the integral.

- x dx

A)
B)
C)
D)

Question 22

Evaluate the integral.

- 3x dx

A)
B)
C)
D)

Question 23

Evaluate the integral.

-

A)
B)
C)
D)

Question 24

Evaluate the integral.

-

A) 13 sin x - x cos x + C
B) 13 sin x + 13x cos x + C
C) 13 sin x - 13 cos x + C
D) 13 sin x - 13x cos x + C

Question 25

Evaluate the integral.

-

A)
B)
C)
D)

Question 26

Evaluate the integral.

-

A)
B)
C)
D)

Question 27

Evaluate the integral.

-

A)
B)
C)
D)

Question 28

Evaluate the integral.

-

A)
B)
C)
D)

Question 29

Evaluate the integral.

-

A)
B)
C)
D)

Question 30

Evaluate the integral.

-

A)
B)
C)
D)

Question 31

Evaluate the integral.

- (Give your answer in exact form.)

A) -
B) -
C)
D) -

Question 32

Evaluate the integral.

-

A) 40.2
B) 6.70
C) 55.2
D) 9.48

Question 33

Evaluate the integral.

-

A) 6.68
B) 2.68
C) 4.6
D) 0.68

Question 34

Evaluate the integral.

-ln 2x dx

A) 51.35
B) 37.13
C) 38.91
D) -19.37

Question 35

Solve the problem.

-Find the volume of the solid generated by revolving the region bounded by the curve the and the vertical line about the x-axis.

A) $\pi$ e - 1)
B) 2 $\pi$ ( - 1)
C) $\pi$ e
D) $\pi$ ( - 1)

Question 36

Solve the problem.

-Find the volume of the solid generated by revolving the region bounded by the curve and the about the x-axis.

A) 16
B) 16 $\pi$
C) 8
D) 8

Question 37

Solve the problem.

-Find the volume of the solid generated by revolving the region in the first quadrant bounded by and the from to about the

A) 14 $\pi$ ln 7
B) 2 $\pi$ ( 7ln 7 - 7)
C) 2 $\pi$ ( 7ln 7 - 6)
D) 7 $\pi$ ln 7

Question 38

Solve the problem.

-Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = , and the line x = ln 6 about the line x = ln 6.

A) 2 $\pi$ ( 5 + ln 6)
B) 2 $\pi$ ( 5 - ln 6)
C) 2 $\pi$ ( 6 - ln 6)
D) 2 $\pi$ (6 - ln 7)

Question 39

Solve the problem.

-Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = , and the line x = 3 about the y-axis.

A) $\pi$ (1 - 11 )
B) $\pi$ (1 - 12 )
C) - $\pi$ (1 + 13 )
D) $\pi$ (1 - 13 )

Question 40

Solve the problem.

-Find the volume of the solid generated by revolving the region in the first quadrant bounded by the x-axis and the curve y = sin 3x, 0 $\le$ x $\le$ $\pi$ / 3 about the line x = $\pi$ / 3.

A)
B) $\pi$
C)
D) - $\pi$

Question 41

Solve the problem.

-Find the volume of the solid generated by revolving the region in the first quadrant bounded by the x-axis and the curve y = x cos x, 0 $\le$ x $\le$ $\pi$ /2 about the y-axis.

A) - 8 $\pi$
B) - 4 $\pi$
C) + 2 - 4 $\pi$
D) - 4 $\pi$

Question 42

Use integration by parts to establish a reduction formula for the integral.

-

A)
B)
C)
D)

Question 43

Use integration by parts to establish a reduction formula for the integral.

-

A)
B)
C)
D)

Question 44

Use integration by parts to establish a reduction formula for the integral.

-

A)
B)
C)
D)

Question 45

Use integration by parts to establish a reduction formula for the integral.

-

A)
B)
C)
D)

Question 46

Use integration by parts to establish a reduction formula for the integral.

-

A)
B)
C)
D)

Question 47

Use integration by parts to establish a reduction formula for the integral.

- , n $\neq$ 1

A)
B)
C)
D)

Question 48

Use integration by parts to establish a reduction formula for the integral.

- , n $\neq$ 1

A)
B)
C)
D)

Question 49

Use integration by parts to establish a reduction formula for the integral.

- , n $\neq$ 1

A)
B)
C)
D)

Question 50

Use integration by parts to establish a reduction formula for the integral.

- , n $\neq$ 1

A)
B)
C)
D)

Question 51

Use integration by parts to establish a reduction formula for the integral.

-

A)
B)
C)
D)

Question 52

Evaluate the integral by using a substitution prior to integration by parts.

-

A)
B)
C)
D)

Question 53

Evaluate the integral by using a substitution prior to integration by parts.

-

A)
B)
C)
D)

Question 54

Evaluate the integral by using a substitution prior to integration by parts.

-

A)
B)
C)
D)

Question 55

Solve the problem.

-Find the area between y = (x - 2)e^x and the x-axis from x = 2 to x = 6.

A) e⁶ + e²
B) 3e⁶
C) 3e⁶ + e²
D) e⁶ - e²

Question 56

Solve the problem.

-The charge q (in coulombs) delivered by a current i (in amperes) is given by where t is the time (in seconds). A damped-out periodic wave form has current given by Find a formula for the charge delivered over time t.

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

Question 57

Solve the problem.

-The voltage v (in volts) induced in a tape head is given by where t is the time (in seconds). Find the average value of v over the interval from t = 0 to t = 4. Round to the nearest volt.

A) 183,853 volts
B) 2,559,851 volts
C) 28,130 volts
D) 30 volts

Question 58

Evaluate the integral.

-

A) 0
B)
C)
D)

Question 59

Evaluate the integral.

- dx

A)
B)
C)
D)

Question 60

Evaluate the integral.

-

A) 0
B)
C)
D)

Question 61

Evaluate the integral.

-

A)
B)
C)
D) -

Question 62

Evaluate the integral.

-

A)
B)
C)
D)

Question 63

Evaluate the integral.

-

A)
B) -
C)
D) -

Question 64

Evaluate the integral.

-

A)
B)
C)
D)

Question 65

Evaluate the integral.

- cos 8 $\theta$ d $\theta$

A)
B)
C)
D)

Question 66

Evaluate the integral.

-

A)
B)
C)
D)

Question 67

Evaluate the integral.

-dx

A)
B)
C)
D)

Question 68

Evaluate the integral.

-

A)
B)
C)
D)

Question 69

Evaluate the integral.

-

A)
B)
C)
D)

Question 70

Evaluate the integral.

-

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

Question 71

Evaluate the integral.

-

A)
B)
C)
D)

Question 72

Evaluate the integral.

-

A)
B)
C)
D)

Question 73

Evaluate the integral.

-

A) -
B) -
C)
D) -

Question 74

Evaluate the integral.

-

A)
B)
C)
D)

Question 75

Evaluate the integral.

- Give your answer in exact form.

A)
B)
C)
D)

Question 76

Evaluate the integral.

-

A)
B)
C)
D)

Question 77

Evaluate the integral.

-

A) 4
B) 2
C) 1
D) 0

Question 78

Evaluate the integral.

-

A) 2
B)
C) 2
D)

Question 79

Evaluate the integral.

- dx

A)
B)
C) 0
D) 2

Question 80

Evaluate the integral.

-

A) 2
B) 1
C) 2 +
D) 2 -