Deck 5: Integration

Question 1

Find the function satisfying the given conditions.

A)
B)
C)
D)

Answer 1

C

Question 2

Suppose that a car can accelerate from mph to mph in seconds. Assuming a constant acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the seconds.

A) Acceleration = m/s2²; distance = miles
B) Acceleration = m/s2²; distance = miles
C) Acceleration = m/s2²; distance = miles
D) Acceleration = m/s2²; distance = miles

Answer 2

C

Question 3

Suppose that a car can come to rest from mph in seconds. Assuming a constant (negative) acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the seconds (i.e., the stopping distance).

A) Acceleration = m/s²; distance = miles
B) Acceleration = m/s²; distance = miles
C) Acceleration = m/s²; distance = miles
D) Acceleration = m/s²; distance = miles

Answer 3

B

Question 4

Find the general antiderivative.

A)
B)
C)
D)

Question 5

Find the function satisfying the given conditions.

A)
B)
C)
D)

Question 6

Find all functions satisfying the given conditions.

A)
B)
C)
D)

Question 7

Find the general antiderivative.

A)
B)
C)
D)

Question 8

Find an antiderivative by reversing the chain rule, product rule or quotient rule.

A)
B)
C)
D)

Question 9

Find the general antiderivative.

A)
B)
C)
D)

Question 10

Determine the position function if the velocity function is and the initial position is .

A)
B)
C)
D)

Question 11

Find an antiderivative by reversing the chain rule, product rule or quotient rule.

A)
B)
C)
D)

Question 12

Sketch a graph of a function corresponding to the given graph of .

Question 13

Determine the position function if the acceleration function is , the initial velocity is , and the initial position is .

A)
B)
C)
D)

Question 14

Find all functions satisfying the given conditions.

A)
B)
C)
D)

Question 15

Sketch a graph of a function corresponding to the given graph of .

Question 16

The following table shows the velocity of a falling object at different times. For each time interval, estimate the distance fallen and the acceleration. Round to two decimal places.

Question 17

Find an antiderivative by reversing the chain rule, product rule, or quotient rule.

Question 18

Find the general antiderivative.

A)
B)
C)
D)

Question 19

Find the general antiderivative.

A)
B)
C)
D)

Question 20

Find the general antiderivative.

A)
B)
C)
D)

Question 21

Translate into summation notation.

A)
B)
C)
D)

Question 22

Use summation rules to compute the sum.

A) 2264
B) 30,784
C) 39,964
D) 2804

Question 23

Use formulas to compute the sum.

A)
B)
C)
D)

Question 24

Write out all terms and compute the sum.

A)
B)
C)
D)

Question 25

Use summation rules to compute the sum.

A)
B)
C)
D)

Question 26

Compute the sum and the limit of the sum as .

A) Sum = ; limit of sum as is
B) Sum = ; limit of sum as is
C) Sum = ; limit of sum as is
D) Sum = ; limit of sum as is

Question 27

Use mathematical induction to prove that for all integers .

Question 28

List the evaluation points corresponding to the midpoint of each subinterval, and evaluate the corresponding Riemann sum. Round the sum to two decimal places.

A) Evaluation points:
Riemann sum:
B) Evaluation points:
Riemann sum:
C) Evaluation points:
Riemann sum:
D) Evaluation points:
Riemann sum:

Question 29

Use summation rules to compute the sum.

A)
B)
C)
D)

Question 30

The following table shows the acceleration of a car moving in a straight line. If the car is traveling ft/s at time , estimate the speed and distance traveled at each time.

Question 31

Compute the sum and the limit of the sum as .

A) Sum = ; limit of sum as is
B) Sum = ; limit of sum as is
C) Sum = ; limit of sum as is
D) Sum = ; limit of sum as is

Question 32

Compute the sum of the form for the given function and -values, with equal to the difference in adjacent 's. ;

A)
B)
C)
D)

Question 33

Translate the following calculation into summation notation and then compute the sum. The sum of the squares of the first positive integers.

A)
B)
C)
D) sum =

Question 34

Write out all terms and compute the sum.

A)
B)
C)
D)

Question 35

Use summation rules to compute the sum.

A)
B)
C)
D)

Question 36

Translate the following calculation into summation notation and then compute the sum. Round to two decimal places. The square root of the sum of the first positive integers.

A) sum =
B) sum =
C)
D)

Question 37

Suppose that a runner has velocity mph for minutes, velocity mph for minutes, velocity mph for minutes, and velocity mph for minutes. Find the distance run. Round to two decimal places.

A) miles
B) miles
C) miles
D) miles

Question 38

Suppose that a car has velocity mph for hours, velocity mph for hours, velocity mph for minutes, and velocity mph for hours. Find the distance traveled. Round to two decimal places.

A) miles
B) miles
C) miles
D) miles

Question 39

The table shows the velocity of a projectile at various times. Estimate the distance traveled. Round to two decimal places.

Question 40

Compute the sum of the form for the given function and -values, with equal to the difference in adjacent 's. ;

A)
B)
C)
D)

Question 41

List the evaluation points corresponding to the midpoint of each subinterval, sketch the function and corresponding approximating rectangles and evaluate the corresponding Riemann sum. Round the sum to two decimal places.

Question 42

Approximate the area under the curve on the given interval using rectangles and left-endpoint evaluation. Round to three decimal places. on ,

A)
B)
C)
D)

Question 43

Evaluate the integral by computing the limit of Riemann sums.

A)
B)
C)
D)

Question 44

Use the Midpoint Rule to estimate the value of the integral (obtain two digits of accuracy).

A) 1.20
B)
C) 0.77
D) 0.43

Question 45

Approximate the area under the curve on the given interval using rectangles and right-endpoint evaluation. Round to three decimal places. on ,

A)
B)
C)
D)

Question 46

Approximate the area under the curve on the given interval using rectangles and right-endpoint evaluation. Round to three decimal places. on ,

A) 58.704
B) 70.381
C) 63.000
D) 61.698

Question 47

Use Riemann sums and a limit to compute the exact area under the curve. on

A)
B)
C)
D)

Question 48

Use the given function values to estimate the area under the curve using left-endpoint and right-endpoint evaluation. Round to two decimal places.

A) Left-endpoint estimate is ; right-endpoint estimate is
B) Left-endpoint estimate is ; right-endpoint estimate is
C) Left-endpoint estimate is ; right-endpoint estimate is
D) Left-endpoint estimate is ; right-endpoint estimate is

Question 49

Use the Midpoint Rule to estimate the value of the integral (obtain two digits of accuracy).

A)
B)
C)
D)

Question 50

Approximate the area under the curve on the given interval using rectangles and midpoint evaluation. Round to three decimal places. on ,

A)
B)
C)
D)

Question 51

Write the given (signed) area as an integral or sum of integrals. The area above the -axis and below

A)
B)
C)
D)

Question 52

Approximate the area under the curve on the given interval using rectangles and left-endpoint evaluation. Round to three decimal places. on ,

A)
B)
C)
D)

Question 53

Use Riemann sums and a limit to compute the exact area under the curve. on

Question 54

Evaluate the integral by computing the limit of Riemann sums.

A)
B)
C)
D)

Question 55

List the evaluation points corresponding to the midpoint of each subinterval, and evaluate the corresponding Riemann sum. Round the sum to two decimal places.

A) Evaluation points:
Riemann sum:
B) Evaluation points:
Riemann sum:
C) Evaluation points:
Riemann sum:
D) Evaluation points:
Riemann sum:

Question 56

Write the given (signed) area as an integral or sum of integrals. The area below the -axis and above

A)
B)
C)
D)

Question 57

Approximate the area under the curve on the given interval using rectangles and midpoint evaluation. Round to three decimal places. on ,

A) 1.000
B) 0.020
C) 0.750
D) 0.667

Question 58

Give an area interpretation of the integral.

Question 59

Use Riemann sums and a limit to compute the exact area under the curve. on

A)
B)
C)
D)

Question 60

Use Riemann sums and a limit to compute the exact area under the curve. on

Question 61

Use the Integral Mean Value Theorem to estimate the value of the integral.

Question 62

Compute , given

A)
B)
C)
D)

Question 63

Write the given (total) area as an integral or sum of integrals. The area between and the -axis for .

A)
B)
C)
D)

Question 64

Suppose that, for a particular population of organisms, the birth rate is given by organisms per month and the death rate is given by organisms per month. Explain why represents the net change in population in the first 12 months. Determine for which values of it is true that . At which times is the population increasing? Decreasing? Determine the time at which the population reaches a maximum.

Question 65

Compute the average value of the function on the given interval.

A)
B)
C)
D)

Question 66

Use the Integral Mean Value Theorem to estimate the value of the integral.

Question 67

Use the graph to determine whether is positive or negative.

A) Positive
B) Negative

Question 68

Use Part I of the Fundamental Theorem of Calculus to compute the integral exactly.

A)
B)
C)
D)

Question 69

Find a value of that satisfies the conclusion of the Integral Mean Value Theorem.

A)
B)
C)
D)

Question 70

Find a value of that satisfies the conclusion of the Integral Mean Value Theorem.

A)
B)
C)
D)

Question 71

Write the given (total) area as an integral or sum of integrals. The area between and the -axis for .

A)
B)
C)
D)

Question 72

Write the expression as a single integral.

A)
B)
C)
D)

Question 73

Write the expression as a single integral.

A)
B)
C)
D)

Question 74

Use the graph to determine whether is positive or negative.

A) Positive
B) Negative

Question 75

Use the given velocity function and initial position to estimate the final position . Round to two decimal places.

A)
B)
C)
D)

Question 76

Use the graph to determine whether is positive or negative.

A) Positive
B) Negative

Question 77

Use the given velocity function and initial position to estimate the final position . Round to two decimal places.

A)
B)
C)
D)

Question 78

Compute the average value of the function on the given interval.

A)
B)
C)
D)

Question 79

Sketch the area corresponding to the integral.

Question 80

The impulse-momentum equation states the relationship between a force applied to an object of mass and the resulting change in velocity of the object. The equation is , where . Suppose that the force of a golf club on a ball is approximately thousand pounds for between 0 and seconds. Using slugs for the mass of a golf ball, estimate the change in velocity (in ft/s). Round to 2 decimal places.

A) ft/s
B) ft/s
C) ft/s
D) ft/s