Deck 4: Integrals

Question 1

Find the indefinite integral.

A)
B)
C)
D)

Answer 1

Question 2

Evaluate the integral.

Answer 2

Question 3

Find the indefinite integral.

A)
B)
C)
D)

Answer 3

Question 4

Evaluate the indefinite integral.

A)
B)
C)
D)
E)

Question 5

Evaluate the definite integral.

A)-2
B)3
C)0
D)1
E)-0.5

Question 6

Evaluate the indefinite integral.

A)
B)
C)
D)
E)

Question 7

Evaluate the integral by making the given substitution.

A)
B)
C)
D)
E)

Question 8

Evaluate the integral.

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

Question 9

Find the integral using the indicated substitution. ,

A)
B)
C)
D)

Question 10

Find the indefinite integral.

A)
B)
C)
D)

Question 11

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

A)
B)
C)
D)
E)

Question 12

Evaluate the definite integral.

Question 13

Evaluate the integral by making the given substitution. ,

A)
B)
C)
D)
E)

Question 14

Evaluate the integral if it exists.

A)
B)
C)0
D)
E)none of these

Question 15

Evaluate the indefinite integral.

Question 16

Find the indefinite integral.

A)
B)
C)
D)

Question 17

Evaluate the indefinite integral.

A)
B)
C)
D)
E)

Question 18

Find the indefinite integral.

A)
B)
C)
D)

Question 19

Find the integral using the indicated substitution. ,

A)
B)
C)
D)

Question 20

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

A)
B)
C)
D)
E)

Question 21

The marginal cost of manufacturing x yards of a certain fabric is in dollars per yard. Find the increase in cost if the production level is raised from yards to yards.

A)
B)
C)
D)
E)

Question 22

Find the indefinite integral.

A) + 5x + C
B)
C) + 5x + C
D)

Question 23

The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure) is given by the integral . Find the area.

A)6.25
B)125
C)
D)
E)45.6

Question 24

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.

A)100 m
B)72 m
C)36 m
D)64 m
E)68 m

Question 25

Find the indefinite integral.

Question 26

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. 0 0
60 10 70 20 80 30 90 40 100 50

A)1.8 miles
B)0.8 miles
C)1.2 miles
D)0.6 miles
E)2.4 miles

Question 27

If 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 and ?

A)
B)
C)

Question 28

Find the indefinite integral.

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

Question 29

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

A)3
B)-12
C)12
D)-3

Question 30

Evaluate the integral.

A)1.000
B)-0.500
C)0.250
D)-1.000
E)

Question 31

Find the general indefinite integral.

A)
B)
C)
D)
E)

Question 32

Evaluate the integral.

Question 33

Evaluate the integral. The choices are rounded to the nearest hundredth.

A)109.00
B)
C)102.33
D)123.67
E)209.00

Question 34

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

A)
B)
C)
D)
E)

Question 35

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)
B)
C)
D)
E)

Question 36

Show that by interpreting the definite integral geometrically.

Question 37

Evaluate the definite integral.

A)3.25
B)
C)
D)0.35
E)

Question 38

Find the indefinite integral.

Question 39

Evaluate the integral.

A)
B)
C)
D)
E)

Question 40

Evaluate the integral.

A)
B)
C)
D)
E)

Question 41

Evaluate the integral.

A)-14
B)-11
C)10
D)14

Question 42

Evaluate the integral.

A)
B)
C)
D)
E)

Question 43

Find the derivative of the function.

Question 44

Find by evaluating the integral using Part 2 of the Fundamental Theorem and then differentiating.

Question 45

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

Question 46

Evaluate the integral.

Question 47

Find the general indefinite integral.

Question 48

Find the area of the region that lies to the right of the y-axis and to the left of the parabola .

Question 49

Find a function f (x) such that for and some number
a.

Question 50

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

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

Question 51

Find the derivative of the function.

Question 52

Find the interval on which the curve is concave downward.

Question 53

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.
Round your answer to the nearest tenth. 0
0
60 10 70 20 80 30 90 40 100 50

Question 54

Evaluate the integral.

Question 55

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

A)1.500
B)1.450
C)-0.500
D)- 1.500
E)0.500

Question 56

Use the following property of the definite integral to estimate the definite integral : If on [a, b], then

A)
B)
C)
D)

Question 57

Find the derivative of the function.

A)
B)
C)
D)

Question 58

Evaluate the indefinite integral.

Question 59

If where find .

A)
B)
C)
D)
E)

Question 60

Let .
a.Use Part 1 of the Fundamental Theorem of Calculus to find .
b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x).
c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1
If f is continuous on [a, b], then the function F defined by
is differentiable on (a, b), and
The Fundamental Theorem of Calculus, Part 2
If f is continuous on [a, b], then
where F is any antiderivative of f, that is, .

Question 61

Use the graph of f shown in the figure to evaluate the integral by interpreting it geometrically.

A)
B)
C)
D)

Question 62

Given that , find .

Question 63

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

Question 64

Use the Midpoint Rule with n = 10 to approximate the integral.

A)
B)
C)
D)
E)

Question 65

Evaluate the integral by interpreting it in terms of areas.

A)
B)
C)
D)
E)

Question 66

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

A)-
B)
C)-
D)

Question 67

If , find the Riemann sum with n = 5 correct to 3 decimal places, taking the sample points to be midpoints.

Question 68

Use the Midpoint Rule with to approximate the integral. Round the answer to 3 decimal places.

Question 69

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].

A)
B)
C)
D)

Question 70

Evaluate by interpreting it in terms of areas.

Question 71

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

Question 72

Express the sum as a single integral in the form .

Question 73

Use to evaluate the integral.

A)
B)22
C)54
D)

Question 74

If and , find .

A)
B)
C)
D)
E)

Question 75

Evaluate the Riemann sum for , with four subintervals, taking the sample points to be right endpoints.

Question 76

A table of values of an increasing function is shown. Use the table to find an upper estimate of . -49 -38 -23 2 13 31

Question 77

Evaluate the Riemann sum for with four subintervals, taking the sample points to be right endpoints.

A)
B)
C)
D)
E)

Question 78

The table gives the values of a function obtained from an experiment. Use the values to estimate using three equal subintervals with left endpoints.
w
0
1
2
3
4
5
6
f (w)
9.7
9.1
7.7
6.1
4.2
-6.6
-10.3

Question 79

Use the Midpoint Rule with n = 5 to approximate the integral. Round your answer to three decimal places.

A)
B)
C)
D)
E)

Question 80

Use the given graph of to find the Riemann sum with six subintervals. Take the sample points to be left endpoints.

A)4
B)6
C)8
D)3.5
E)4.5