Deck 7: Integration

Question 1

Find the limit of s(n) as n .

A)6/7
B)12/7
C)1/7
D)6
E)unbounded

Answer 1

unbounded

Question 2

Use the properties of summation and Theorem 4.2 to evaluate the sum.

A)1386
B)1610
C)1162
D)1080
E)1161

Answer 2

1162

Question 3

Find the indefinite integral .

A)
B)
C)
D)
E)

Answer 3

Question 4

Find the limit of s(n) as n .

A)3/4
B)3/2
C)1/4
D)unbounded
E)3

Question 5

An evergreen nursery usually sells a certain shrub after 4 years of growth and shaping. The growth rate during those 4 years is approximated by where t is the time in years and h is the height in centimeters. The seedlings are 11 centimeters tall when planted . Find the height after t years.

A)
B)
C)
D)
E)

Question 6

Find the indefinite integral .

A)
B)
C)
D)
E)

Question 7

Find the indefinite integral and check the result by differentiation.

A)
B)
C)
D)
E)

Question 8

Find the indefinite integral .

A)
B)
C)
D)
E)none of the above

Question 9

Use sigma notation to write the sum .

A)
B)
C)
D)
E)

Question 10

Find the general solution of the differential equation below and check the result by differentiation.

A)
B)
C)
D)
E)

Question 11

The height above the ground of an object thrown upward from a point feet above the ground with an initial velocity of feet per second is given by the function . A balloon, rising vertically with a velocity of 20 feet per second, releases a sandbag at the instant it is 44 feet above the ground. How many seconds after its release will the bag strike the ground? Round your answer to three decimal places.

A)2.289 seconds
B)2.397 seconds
C)1.375 seconds
D)1.147 seconds
E)1.298 seconds

Question 12

Use the properties of summation and Theorem 4.2 to evaluate the sum.

A)4930
B)335
C)10,409
D)5555
E)5533

Question 13

Find the sum given below.

A)518
B)224
C)350
D)154
E)220

Question 14

Find the sum given below.

A)175
B)140
C)105
D)135
E)165

Question 15

A ball is thrown vertically upwards from a height of 7 ft with an initial velocity of 45 ft per second. How high will the ball go? Note that the acceleration of the ball is given by feet per second per second.

A)101.9219 ft
B)30.7305 ft
C)38.6406 ft
D)87.9219 ft
E)103.7219 ft

Question 16

The maker of an automobile advertises that it takes 11 seconds to accelerate from 30 kilometers per hour to 75 kilometers per hour. Assuming constant acceleration, compute the acceleration in meters per second per second. Round your answer to three decimal places.

A)1.250 m/sec²
B)2.652 m/sec²
C)2.917 m/sec²
D)2.557 m/sec²
E)1.136 m/sec²

Question 17

The rate of growth of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days That is, . The initial size of the population is 300. After one day the population has grown to 400. Estimate the population after 9 days. Round your answer to the nearest integer.

A) bacteria
B) bacteria
C) bacteria
D) bacteria
E) bacteria

Question 18

Use the properties of summation and Theorem 4.2 to evaluate the sum.

A)4411
B)77,275
C)4319
D)65,016
E)77,259

Question 19

Find the general solution of the differential equation below and check the result by differentiation.

A)
B)
C)
D)
E)

Question 20

Find the sum given below.

A)
B)
C)
D)
E)

Question 21

The graph of f consists of line segments, as shown in the figure. Evaluate the definite integral using geometric formulas.

A)-2
B)0
C)-3
D)-4
E)-1

Question 22

Find the limit .

A)48
B)24
C)14
D)28
E)12

Question 23

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

A)9
B)4
C)5.5
D)1
E)33.5

Question 24

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

A)
B)
C)
D)
E)

Question 25

Write the limit as a definite integral on the interval where c_i is any point in the ith subinterval.

A)
B)
C)
D)
E)

Question 26

Evaluate the following definite integral by the limit definition.

A)
B)
C)
D)
E)

Question 27

Evaluate the integral given

A)12
B)18
C)28
D)-18
E)45

Question 28

Write the limit as a definite integral on the interval where is any point in the subinterval.

A)
B)
C)
D)
E)

Question 29

Use the summation formulas to rewrite the expression without the summation notation.

A)
B)
C)
D)
E)

Question 30

Evaluate the following definite integral by the limit definition.

A)-351
B)-339
C)351
D)339
E)-363

Question 31

The graph of the function is given below. Which of the following definite integrals yields the area of the shaded region?

A)
B)
C)
D)
E)

Question 32

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.

A)2643
B)-2541
C)2541
D)5235
E)51

Question 33

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral.

A)
B)
C)
D)
E)

Question 34

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.

A)10
B)20
C)-6
D)12
E)-11

Question 35

The graph of the function is given below. Which of the following definite integrals yields the area of the shaded region?

A)
B)
C)
D)
E)

Question 36

Evaluate the integral given

A)8
B)-73
C)-18
D)-40
E)-13

Question 37

The diagram below shows upper and lower sums for the function using 4 subintervals. Use upper and lower sums to approximate the area of the region using the 4 subintervals.

A)lower: 1.019 ; upper: 1.769
B)lower: 1.269 ; upper: 1.519
C)lower: 5.076 ; upper: 6.076
D)lower: 2.538 ; upper: 3.038

Question 38

Use the limit process to find the area of the region between the graph of the function and x-axis over the interval .

A)
B)
C)
D)
E)

Question 39

Write the following limit as a definite integral on the interval [5 , 11], where c_i is any point in the ith subinterval.

A)
B)
C)
D)
E)

Question 40

Evaluate the definite integral of the algebraic function. Use a graphing utility to verify your results.

A)
B)
C)
D)
E)

Question 41

Find the indefinite integral of the following function and check the result by differentiation.

A)
B)
C)
D)
E)

Question 42

Find the indefinite integral of the following function and check the result by differentiation.

A)
B)
C)
D)
E)

Question 43

Find F'(x) given .

A)
B)
C)
D)
E)

Question 44

The total cost C (in dollars) of purchasing and maintaining a piece of equipment for x years is Perform the integration to write C as a function of x.

A)
B)
C)
D)
E)

Question 45

Find the indefinite integral .

A)
B)
C)
D)
E)

Question 46

Find the indefinite integral .

A)
B)
C)
D)
E)

Question 47

Find the average value of on the interval .

A)
B)
C)
D)
E)

Question 48

Solve the differential equation.

A)
B)
C)
D)
E)

Question 49

Find the area of the region bounded by the graphs of the equations . Round your answer to the nearest whole number.

A)12
B)53
C)29
D)9
E)128

Question 50

Suppose that the probability that a person will remember between 100a% and 100b% of material learned in an experiment is where x represents the proportion remembered. Determine from the figure below, the probability that a randomly chosen individual will recall between 30% and 75% of the material? Express your answer as a percent rounded to three decimal places.

A)12.100%
B)154.300%
C)58.400%
D)3.300%
E)12.300%

Question 51

Evaluate the following definite integral. Use a graphing utility to check your answer.

A)
B)
C)
D)
E)

Question 52

Find the indefinite integral of the following function and check the result by differentiation.

A)
B)
C)
D)
E)

Question 53

Find the average value of the function over the interval .

A)
B)
C)
D)
E)

Question 54

Use the Trapezoid Rule to approximate the value of the definite integral wth . Round your answer to four decimal places.

A)6.3750
B)33.0000
C)6.7500
D)7.8750
E)8.2500

Question 55

The rate of depreciation of a machine is inversely proportional to the square of where V is the value of the machine t years after it was purchased. The initial value of the machine was and its value decreased in the first year. Estimate its value after 5 years. Round your answer to the nearest integer.

A)$500,000
B)$285,714
C)$571,428
D)$485,714
E)$371,429

Question 56

Find F'(x) given .

A)
B)
C)
D)
E)

Question 57

The rate of disbursement of a 2 million dollar federal grant is proportional to the square of Time t is measured in days and is the amount that remains to be disbursed. Find the amount that remains to be disbursed after 60 days. Assume that all the money will be disbursed in 200 days.

A)$686,000
B)$1,029,000
C)$50,700
D)$16,900
E)$25,350

Question 58

Find the indefinite integral .

A)
B)
C)
D)
E)

Question 59

Solve the differential equation.

A)
B)
C)
D)
E)

Question 60

Determine the area of the given region.

A)
B)
C)
D)
E)

Question 61

Use Simpson's Rule to approximate the value of the definite integral with . Round your answer to four decimal places.

A)48.4495
B)59.3159
C)62.6492
D)69.3159
E)52.6492

Question 62

Use a computer algebra system and Simpson's Rule with to approximate t in the integral equation . Round your answer to three decimal places.

A)6.385
B)6.045
C)5.715
D)6.008
E)5.985

Question 63

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using Simpson's Rule.

A)5
B)12
C)7
D)15
E)9

Question 64

Use Simpson's Rule with to approximate using the equation . Round your answer to five decimal places.

A)3.14441
B)3.13877
C)3.14903
D)3.14159
E)3.13415