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Chapter 5 Early Transcendentals

front 1

The velocity graph of a braking car is shown. Use it to estimate to the nearest foot the distance traveled by the car while the brakes are applied. Use a left sum with n = 7.

back 1

19

front 2

Evaluate by interpreting it in terms of areas.

back 2

front 3

Express the limit as a definite integral on the given interval.

back 3

front 4

Find an expression for the area under the graph of f as a limit. Do not evaluate the limit.

f(x) = √sinx x, 0 ≤ x ≤ π

back 4

front 5

Find the limit.

back 5

3

front 6

Find gt(x) by evaluating the integral using Part 2 of the Fundamental Theorem and then differentiating.

back 6

6 + cos x

front 7

An animal population is increasing at a rate of 32 + 36t per year (where t is measured in years). By how much does the animal population increase between the fourth and tenth years?

back 7

1704

front 8

Evaluate the definite integral.

back 8

0

front 9

Evaluate the integral.

back 9

18.75

front 10

Evaluate the indefinite integral.

back 10

2/5 (x2 + 3)5 + C

front 11

Use the definition of area to find the area of the region under the graph of f on [a, b] using the indicated choice of ck.

f(x) = x2, [0,6], ck is the left endpoint

back 11

72

front 12

Evaluate the limit after first finding the sum (as a function of n) using the summation formulas.

back 12

76/3

front 13

The graph of a function f on the interval [0, 8] is shown in the figure. Compute the Riemann sum for f on [0, 8] using four subintervals of equal length and choosing the evaluation points to be (a) the left endpoints, (b) the right endpoints, and (c) the midpoints of the subintervals.

back 13

a. 18
b. 10
c. 10

front 14

You are given function f defined on an interval [a, b], the number n of subintervals of equal length ∆x = (b-a)/n, and the evaluation points ck in [xk -1, xk].
(a) Sketch the graph of f and the rectangles associated with the Riemann sum for f on [a, b], and
(b) find the Riemann sum.

f(x) = 2x - 3, [0,2], n=4, ck is the right endpoint

back 14

front 15

Evaluate

back 15

4

front 16

back 16

a. 5x2
b. 5/3x3 - 625/3
c. 5x2

front 17

Evaluate the integral.

back 17

2 - √2

front 18

The acceleration function of a body moving along a coordinate line is

a(t) = -7 cos 2t - 8 sin 2t t ≥ 0

Find its velocity and position functions at any time t if it is located at the origin and has an initial velocity of 4 m/sec.

back 18

v(t) = -7/2 sin 2t + 4 cos 2t, s(t) = 7/4 cos 2t + 2 sin 2t - 7/4

front 19

Find the indefinite integral.

back 19

2/15(3x + 16)√(x-8)3 + C

front 20

Show by interpreting the definite integral geometrically.

back 20

A sketch of the area between the curve and the x-axis, shows that the area below the x-axis is equal to the area above the x-axis.

front 21

The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds.

back 21

17.65

front 22

By reading values from the given graph of f, use five rectangles to find a lower estimate, to the nearest whole number, for the area from 0 to 10 under the given graph of f.

back 22

21

front 23

Approximate the area under the curve y = 2/x2 from 1 to 2 using ten approximating rectangles of equal widths and right endpoints. Round the answer to the nearest hundredth.

back 23

0.93

front 24

The velocity graph of a braking car is shown. Use it to estimate to the nearest foot the distance traveled by the car while the brakes are applied. Use a left sum with n = 7.

back 24

19

front 25

Find an expression for the area under the graph of f as a limit. Do not evaluate the limit.

f(x) = √sin x, 0 ≤ x ≤ π

back 25

front 26

If f(x) = √x-4, 1≤x≤6, find the Riemann sum with n = 5 correct to 3 decimal places, taking the sample points to be midpoints.

back 26

-10.857

front 27

A table of values of an increasing function f(x) is shown. Use the table to find an upper estimate of:

back 27

-210

front 28

Express the limit as a definite integral on the given interval.

back 28

front 29

Find the area of the region that lies under the given curve.

y = sin x, 0 ≤ x ≤ π/2

back 29

1

front 30

Express the sum as a single integral in the form

back 30

front 31

Find an expression for the area under the graph of f as a limit. Do not evaluate the limit.

f(x) = √sin x, 0 ≤ x ≤ π

back 31

front 32

back 32

43.2

front 33

Find the limit.

back 33

3

front 34

back 34

f(x) = 4x3/2; for a = 25/64

front 35

Evaluate the integral.

back 35

7√3/3 + π/6

front 36

Find the area of the region that lies to the right of the y-axis and to the left of the parabola x = 3y - y2

back 36

9/2

front 37

Evaluate the integral.

back 37

1/3 arctan (e3) - π/12

front 38

Evaluate the definite integral.

back 38

-6

front 39

Evaluate the integral.

back 39

7.5

front 40

Evaluate the integral.

back 40

193/9

front 41

Approximate the area under the curve y = sin x from 0 to π/2 using 8 approximating rectangles of equal widths and right endpoints. The choices are rounded to the nearest hundredth.
a. 3.09
b. 1.09
c. 4.09
d. 0.09
e. 2.09

back 41

b

front 42

Evaluate the integral by interpreting it in terms of areas.

back 42

a

front 43

Evaluate

a. earcsintx/4
b. earcsint
c. earcsinx
d. ex - arcsinx
e. e

back 43

c

front 44

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

a. √x+1/x2+2
b. √x2+1/2
c. √x/2(x2+1)
d. √x/x2+1
e. none of these

back 44

c

front 45

Find the derivative of the function.

a. - 2x/(x2+2)2
b. -2/9
c. 1/3
d.1/x2+2

back 45

d

front 46

An animal population is increasing at a rate of 13 + 51t per year (where t is measured in years). By how much does the animal population increase between the fourth and tenth years?
a. 2220
b. 2240
c. 2270
d. 2320
e. 2230

back 46

a

front 47

Evaluate the integral.
a. 84
b. 94
c. 54
d. 34
e.74

back 47

c

front 48

The velocity function (in meters per second) is given for a particle moving along a line. Find the distance traveled by the particle during the given time interval.

v(t) = 8t - 8, 0 ≤ t ≤ 5

a. 36 m
b. 72 m
c. 100 m
d. 64 m
e. 68 m

back 48

e

front 49

a. 175/6
b. 4
c. 9
d. 4/3
e.6

back 49

d

front 50

Find the indefinite integral

a. 3/7 x7 - 2x4 + 5x + C
b. 5x - 8x4 + 3x7 + C
c. 3/7 x6 - 2x3 + 5x + C
d.5x - 24x2 + 18x5 + C

back 50

a

front 51

Evaluate the definite integral.
a. 0.188
b. 3.25
c. -0.045
d. 0.35
e.2.891

back 51

a

front 52

Find the indefinite integral.

a. 2x + 5/4x4 - 1/4x8 + C
b. 2x + 5/2 x2 - 1/3 x6 + C
c. 2x + 5/4 x4 - 1/4 x8 + C
d. 2x + 5/2x2 - 1/3x6 + C

back 52

d

front 53

Find the indefinite integral

a. x3-25x/x3+25x + C
b. x - 10 arctan(x/5) + C
c. x - 6 arctan(x/5) + C
d.x3-75x/x3+75x + C

back 53

b

front 54

Find the integral.
a. 1/29 e2x (2sin5x - 5cos5x) + C
b. 1/29 e2x (2sin5x - 5cos2x) + C
c. 1/29 e2x (2sin5x - 2cos5x) + C
d. 1/29 e2x (2sin5x - 5cos5x) + C

back 54

a

front 55

Evaluate the indefinite integral.
a. 1/10 cot10x + C
b. 1/10 sin10x + C
c. 1/10 cos10x + C
d. - 1/10 sin10x + C
e. - 1/10 cos10x + C

back 55

e

front 56

Evaluate the integral by making the given substitution.
a. 2/3 (x3 + 2)3/2
b. 2/9 (x3 + 2)1/2 + C
c. - 2/9 (x3 + 2)3/2 + C
d. 2/9 (x3 + 2)3/2 + C
e. 1/9 (x3 + 2)1/2 + C

back 56

d

front 57

Evaluate the integral.

∫2 sin x cos(cos x) dx

a. -2cos(sin x) + C
b. sin(cosx)/2 + C
c. 2sin(cosx) + C
d. -2sin(cosx) + C
e. None of these

back 57

d

front 58

Find the integral.

∫tan3x sec5x dx

a. 1/7 sec7x - 1/5 sec5x + C
b. 1/5 sec5x + 1/3 sec3x + C
c. 1/7 sec7x + 1/5 sec5x + C
d. 1/5 sec5x - 1/3 sec3x + C

back 58

a

front 59

Find the integral using an appropriate trigonometric substitution.

∫x√9-x2 dx

a. 1/3 x2(9 - x2)3/2 + C
b. - 1/3 (9 - x2)3/2 + C
c. - 1/3 x2(9 - x2)3/2 + C
d. 1/3 (9 - x2)3/2 + C

back 59

b

front 60

Find the integral using an appropriate trigonometric substitution.

∫x3/√x2+36 dx

a. 1/3 (x2 + 36)3/2 √x2+36 + C
b. 1/3 (x2 + 72) √x2+36 + C
c. 1/3 (x2 - 72) √x2+36 + C
d. 1/3 (x2 - 36)3/2 √x2+36 + C

back 60

c

front 61

a. 7
b. -13
c. 20
d. 6
e.13

back 61

d

front 62

a. 18
b. 22
c. 54
d. 22/3

back 62

a

front 63

The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression as a definite integral on [a, b].

back 63

d

front 64

back 64

c

front 65

back 65

c

front 66

Evaluate the integral.
a. –14
b. –11
c. 10
d. 14

back 66

c

front 67

The marginal cost of manufacturing x yards of a certain fabric is

Ct(x) = 3 - 0.01x + 0.000006x2

in dollars per yard. Find the increase in cost if the production level is raised from 1500 yards to 5500 yards.
a. $188,000.00
b. $198,000.00
c. $178,000.00
d. $218,000.00
e. $208,000.00

back 67

b

front 68

The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval.

a(t) = t + 4, v(0) = 6, 0 ≤t ≤ 10

a. v(t) = t2/2 + 6t m/s, 576 2/3 m
b. v(t) = t2/2 + 6t m/s, 601 2/3 m
c. v(t) = t2/2 +4t + 6 m/s, 526 2/3 m
d. v(t) = t2/2 +4t + 6 m/s, 426 2/3 m
e. v(t) = t2/2 + 6 m/s, 626 2/3 m

back 68

d

front 69

The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the car.

a. 1.2 miles
b. 1.8 miles
c. 0.8 miles
d. 2.4 miles
e. 0.6 miles

back 69

a

front 70

a. 175/6
b. 4
c. 9
d. 4/3
e. 6

back 70

d

front 71

Find the area of the region under the graph of f on [a, b].

f(x) = x2 - 2x + 4; [-1,2]

a. 3
b. –12
c. 12
d. –3

back 71

c

front 72

a. 6.25
b. 125
c. 25/6
d. 125/6
e. 45.6

back 72

d

front 73

Find the indefinite integral.

∫(4 - 7x4 + 3x6)dx

a. 3/7 x7 - - 7/5 x5 + 4x + C
b. 4x - 28x3 + 18x5 + C
c. 3/7 x6 - 7/5 x4 + 4x + C
d.4x - 7x5 + 3x7 + C

back 73

a

front 74

Find the indefinite integral.

∫cot2x/cos2x dx

a. cos2x + C
b. tan x + C
c. csc2x + C
d.-cotx + C

back 74

d

front 75

Evaluate the integral by making the given substitution.

back 75

d

front 76

Evaluate the indefinite integral.

back 76

c

front 77

Find the indefinite integral.

∫1-cos2x/sinx dx

a. sin x + C
b. 2x + C
c. -csc x + C
d.-cos x + C

back 77

d

front 78

Evaluate the integral.

∫2 sin x cos(cos x) dx

a. -2cos(sin x) + C
b. sin(cos x)/2 + C
c. 2sin(cos x) + C
d. -2sin(cos x) + C
e. None of these

back 78

d

front 79

Find the integral.

back 79

a

front 80

Find the integral using an appropriate trigonometric substitution.

back 80

a

front 81

Estimate to the hundredth the area from 1 to 5 under the graph of f(x) = 5/x using four approximating rectangles and right endpoints. Select the correct answer.
a. 8.03
b. 10.03
c. 7.03
d. 9.03
e. 11.03
f. 6.03

back 81

a

front 82

Determine a region whose area is equal to

back 82

y = tan x, 0 ≤ x ≤ π/5

front 83

Approximate the area under the curve y = sin x from 0 to π/2 using 7 approximating rectangles of equal widths and right endpoints. The choices are rounded to the nearest hundredth.

back 83

1.11

front 84

Evaluate the integral by interpreting it in terms of areas.

back 84

9/2 π

front 85

Evaluate the integral. Select the correct answer.
a. 0.857
b. -0.943
c. 0.557
d. 0.057
e. 1.057

back 85

d

front 86

Evaluate the integral.

back 86

36

front 87

Estimate the area from 0 to 5 under the graph of f(x) = 16 - x2 using five approximating rectangles and right endpoints. Select the correct answer.
a. 25
b. 20
c. 15
d. 125
e. 225

back 87

a

front 88

If ht is a child's rate of growth in pounds per year, which of the following expressions represents the increase in the child's weight (in pounds) between the years 3 and 6?

back 88

front 89

Find the indefinite integral.

∫(8 - 7x3 + 4x6) dx

back 89

4/7 x7 - 7/4 x4 + 8x + C

front 90

Evaluate the definite integral. Select the correct answer.
a. -0.045
b. 0
c. 0.35
d. 3.25
e.2.891

back 90

b

front 91

Find the indefinite integral.

∫(9 - 7x3 + 4x7) dx

back 91

1/2 x8 - 74 x4 + 9x + C

front 92

Find the integral.

∫xe7x dx

back 92

1/49 (7x - 1)e7x + C

front 93

Find the integral using an appropriate trigonometric substitution.

∫x/√16-x2 dx

back 93

- √16-x2 + C

front 94

Find the integral.

∫x tan27x dx

back 94

1/7 x tan 7x + 1/49 ln|cos 7x| - 1/2 x2 + C

front 95

Evaluate the indefinite integral. Select the correct answer.

∫5ecos x sin x dx

a. -5sin(ecos x) + C
b. -ecos x sin x + C
c. -5ecos x + C
d. e5sin x + C
e. 5ecos x sin x + C

back 95

c

front 96

Find the area of the region that lies under the given curve. Round the answer to three decimal places.

y = √5x+2, 0 ≤ x ≤ 1

back 96

2.092

front 97

Find the indefinite integral. Select the correct answer.

2x(4x2 + 2)6 dx

a. 2x2(4x2 + 2)7 + C
b. 1/28 (4x2 + 2)7 + C
c. (4x2 + 2)7 + C
d. x2(4x2 + 2)7 + C

back 97

b

front 98

Find the integral.

∫sin5x cos4x dx

back 98

- 1/9 cos9x + 2/7 cos7x - 1/5 cos5x + C

front 99

Find the integral.

∫tan5x sec x dx

back 99

1/5 sec5x - 2/3 sec3x + sec x + C

front 100

Find the integral. Select the correct answer.

∫tan2x sec6x dx

a. 1/7 tan7x + 2/5 tan5x + 1/3 tan3x + C
b. 1/5 tan5x + 2/3 tan3x - tan x + C
c. 1/7 tan7x + 2/5 tan5x - 1/3 tan3x + C
d. 1/5 tan5x + 2/3 tan3x + tan x + C

back 100

a

front 101

Approximate the area under the curve y = sinx x from 0 to π/2 using 8 approximating rectangles of equal widths and right endpoints. The choices are rounded to the nearest hundredth.
Select the correct answer.
a. 3.09
b. 1.09
c. 4.09
d. 0.09
e. 2.09

back 101

b

front 102

Evaluate the Riemann sum for f(r) = 6 - r2, 0 ≤ r ≤ 2 with four subintervals, taking the sample points to be right endpoints. Select the correct answer.
a. 10.75
b. 9.75
c. 8.25
d. 10.25
e. 9.25

back 102

c

front 103

Evaluate the integral.
Round your answer to the nearest hundredth.

back 103

33.5

front 104

The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression as a definite integral on [a, b].

back 104

front 105

back 105

-5

front 106

Find the area of the region that lies beneath the given curve. Select the correct answer.

y = sin x, 0 ≤ x ≤ π/3

a. 1.500
b. 1.450
c. –0.500
d. – 1.500
e. 0.500

back 106

e

front 107

Find the derivative of the function.

back 107

1/x2+2

front 108

Evaluate the integral. Select the correct answer.
a. –14
b. –11
c. 10
d. 14

back 108

c

front 109

Evaluate the integral.

back 109

0.340

front 110

Evaluate the limit by interpreting it as the limit of a Riemann sum of a function on the interval [a, b].

back 110

243/5

front 111

The marginal cost of manufacturing x yards of a certain fabric is

Ct(x) = 3 - 0.01x + 0.000006x2

in dollars per yard. Find the increase in cost if the production level is raised from 1500 yards to 5500 yards.
Select the correct answer.
a. $188,000.00
b. $198,000.00
c. $178,000.00
d. $218,000.00
e. $208,000.00

back 111

b

front 112

Evaluate the integral if it exists.

∫(5-x/x)2 dx

back 112

x - 10 ln x - 25/x + C

front 113

Evaluate the integral.

back 113

-0.400

front 114

Find the indefinite integral.

∫(5 - 8x3 + 3x6) dx

back 114

3/7 x7 - 2x4 + 5x + C

front 115

Find the integral.

∫x sin 5x dx

back 115

1/25 (sin5x - 5x cos 5x) + C

front 116

Find the integral. Select the correct answer.

∫x tan25x dx

a. 1/2 x tan5x + 1/5 ln|cos5x| - 1/2 x2 + C
b. 1/2 x2 tan5x + 1/5 ln|cos5x| - 1/2 x2 + C
c. 1/5 x tan5x + 1/25 ln|cos5x| - 1/2 x2 + C
d. 1/5 x2 tan5x + 1/25 ln|cos5x| - 1/2 x2 + C

back 116

c

front 117

Evaluate the integral.

back 117

π/24

front 118

Evaluate the indefinite integral.

∫7ecos x sin x dx

back 118

-7ecos x + C

front 119

Find the indefinite integral.

∫1-cos2x/sinx dx

back 119

-cos x + C

front 120

Find the integral.

∫tan3x sec5x dx

back 120

1/7 sec7x - 1/5 sec5x + C

front 121

Use the Midpoint Rule with n = 10 to approximate the integral. Select the correct answer.
a. 7.882848
b. 1.882848
c. 12.882848
d. 10.882848
e.2.882848

back 121

e

front 122

back 122

3√2

front 123

Find the area of the region that lies beneath the given curve.

y = sin x, 0 ≤ x ≤ π/3

back 123

0.500

front 124

Find the derivative of the function.

back 124

1/x2+4

front 125

Find the general indefinite integral. Select the correct answer.

∫sin40t/sin20t dt

a. -cos40t/40 + C
b. sin20t/10 + C
c. sin40t/40 + C
d. -sin40t/40 + C
e. cos40t/10 + C

back 125

b

front 126

Evaluate the integral.

back 126

2π/3

front 127

Evaluate the integral. Select the correct answer.
a. 84
b. 54
c. 34
d. 74
e. 94

back 127

b

front 128

Evaluate the integral.

back 128

24.4

front 129

If ht is a child's rate of growth in pounds per year, which of the following expressions represents the increase in the child's weight (in pounds) between the years 2 and 7?

back 129

front 130

Evaluate the definite integral.

back 130

0.188

front 131

Find the integral using an appropriate trigonometric substitution.

∫x/√4-x2 dx

back 131

-√4-x2 + C

front 132

Find the integral. Select the correct answer.

∫x7 ln x dx

a. 1/64 x8(ln x - 1) + C
b. 1/8 x7 + 1/x + C
c. 1/64 x8(8ln x - 1) + C
d. 1/8 x8(8ln x - 1) + C

back 132

c

front 133

Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calculators after t weeks is

dx/dt = 5700(1 - 140/(t+20)2)

calculators per week. Production approaches 5,700 per week as time goes on, but the initial production is lower because of the workers' unfamiliarity with the new techniques. Find the number of calculators produced from the beginning of the third week to the end of the fourth week. Round the answer to the nearest integer.

back 133

8377

front 134

Evaluate the indefinite integral.

∫cos8x sin x dx

back 134

- 1/9 cos9x + C

front 135

Evaluate the integral by making the given substitution.

∫x2 √x3+6 dx, u = x3 + 6

back 135

2/9 (x3 + 6)3/2 + C

front 136

Evaluate the indefinite integral. Select the correct answer.

∫7+12x/√7+7x+6x2 dx

a. 2 √7+7x+6x2 + C
b. - √7+7x+6x2 + C
c. -5 √7+7x+6x2 + C
d. √7+7x+6x2 + C
e. -2 √7+4x+5x2 + C

back 136

a

front 137

Find the integral using the indicated substitution.

∫tan6x sec2x dx, u = tan x

back 137

1/7 tan7x + C

front 138

Find the indefinite integral.

∫5x/√5-x2 dx

back 138

-5√5-x2 + C

front 139

Find the integral.

∫cos3x sin4x dx

back 139

1/5 sin5x - 1/7 sin7x + C

front 140

Find the integral.

∫tan4x sec4x dx

back 140

1/7 tan7x + 1/5 tan5x + C

front 141

Estimate to the hundredth the area from 1 to 5 under the graph of f(x) = 4/x using four approximating rectangles and right endpoints.

back 141

5.44

front 142

Find the area of the region under the graph of f on [a, b].

f(x) = x2 - 2x + 2; [-1,2]

back 142

6

front 143

Use the Midpoint Rule with n = 5 to approximate the integral. Select the correct answer. Round your answer to three decimal places.
a. 35.909
b. 37.709
c. 36.409
d. 31.409
e. 36.909

back 143

d

front 144

The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression as a definite integral on [a, b]. Select the correct answer.

back 144

d

front 145

back 145

front 146

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

back 146

√x/2(x2+1)

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Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. Select the correct answer.

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c

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Evaluate the integral. Select the correct answer.
a. 0.340
b. 0.111
c. 0.321
d. 0.987
e. 0.568

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a

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Find the general indefinite integral.

∫sin120t/sin60t dt

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sin60t/30 + C

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The marginal cost of manufacturing x yards of a certain fabric is

Ct(x) = 3 - 0.01x + 0.000006x2

in dollars per yard. Find the increase in cost if the production level is raised from 1500 yards to 5500 yards.

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$198,000.00

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Evaluate the integral. Select the correct answer.
a. –0.500
b. –1.000
c. -0.400
d. 0.250
e. 1.000

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c

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Find the indefinite integral.

∫(4 - 7x4 + 3x6) dx

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3/7 x7 - 7/5 x5 + 4x + C

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Find the integral.

∫x sin5x dx

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1/25 (sin5x - 5xcos5x) + C

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Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calculators after t weeks is

dx/dt = 5700(1 - 130/(t+18)2)

calculators per week. Production approaches 5,700 per week as time goes on, but the initial production is lower because of the workers' unfamiliarity with the new techniques. Find the number of calculators produced from the beginning of the third week to the end of the fourth week.

Round the answer to the nearest integer.
a. 8232
b. 7732
c. 8132
d. 8332
e. 8032

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e

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Evaluate the integral by making the given substitution.

∫x2 √x3+2 dx, u = x3 + 2

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2/9 (x3 + 2)3/2 + C

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Evaluate the integral if it exists.

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none of these

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Find the indefinite integral. Select the correct answer.

∫(x2 + 4x - 5)2(2x + 4) dx

a. -2(x2 + 4x - 5)3 + C
b. 2(x2 + 4x - 5)3 + C
c. (x2 + 4x - 5)3 + C
d. 1/3 (x2 + 4x - 5)3 + C

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d

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Evaluate the integral.

∫2sin x cos(cos x) dx

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-2sin(cos x) + C

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Find the integral using an appropriate trigonometric substitution. Select the correct answer.

∫x √9-x2 dx

a. 1/3 x2(9 - x2)3/2 + C
b. -1/3 (9 - x2)3/2 + C
c. -1/3 x2(9 - x2)3/2 + C
d. 1/3 (9 - x2)3/2 + C

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b