230 Chapter 4: Integration
4.1 Antiderivatives and Indefinite Integration
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the general solution of the differential equation below and check the result by
differentiation.
a.
b.
c.
d.
e.
____ 2. Find the general solution of the differential equation below and check the result by
differentiation.
a.
b.
c.
d.
e.
____ 3. Find the indefinite integral .
a.
b.
c.
d.
e. none of the above
4.1 Antiderivatives and Indefinite Integration 231
____ 4. Find the indefinite integral .
a.
b.
c.
d.
e.
____ 5. Find the indefinite integral .
a.
b.
c.
d.
e.
____ 6. Find the indefinite integral .
a.
b.
c.
d.
e.
____ 7. Find the indefinite integral .
a.
b.
c.
d.
e.
____ 8. Find the indefinite integral and check the result by differentiation.
a.
232 Chapter 4: Integration
b.
c.
d.
e.
____ 9. Find the indefinite integral .
a.
b.
c.
d.
e.
____ 10. Find the indefinite integral .
a.
b.
c.
d.
e.
____ 11. Find the indefinite integral .
a.
b.
c.
d.
e.
____ 12. An evergreen nursery usually sells a certain shrub after years of growth and
shaping. The growth rate during those years is approximated by , where t is the time in
years and h is the height in centimeters. The seedlings are centimeters tall when planted .
Find the height after t years.
a.
b.
c.
d.
e.
4.1 Antiderivatives and Indefinite Integration 233
____ 13. An evergreen nursery usually sells a certain shrub after years of growth and
shaping. The growth rate during those years is approximated by , where t is the time in
years and h is the height in centimeters. The seedlings are centimeters tall when planted .
How tall are the shrubs when they are sold?
a. cm
b. cm
c. cm
d. cm
e. cm
____ 14. 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 . After one day the population has grown to . Estimate the
population after days. Round your answer to the nearest integer.
a. bacteria
b. bacteria
c. bacteria
d. bacteria
e. bacteria
____ 15. A ball is thrown vertically upwards from a height of ft with an initial velocity of
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. ft
b. ft
c. ft
d. ft
e. ft
____ 16. The maker of an automobile advertises that it takes seconds to accelerate from
kilometers per hour to kilometers per hour. Assuming constant acceleration, compute the
acceleration in meters per second per second. Round your answer to three decimal places.
a. m/sec2
b. m/sec2
c. m/sec2
d. m/sec2
e. m/sec2
234 Chapter 4: Integration
____ 17. The maker of an automobile advertises that it takes seconds to accelerate from
kilometers per hour to kilometers per hour. Assuming constant acceleration, compute the distance,
in meters, the car travels during the seconds. Round your answer to two decimal places.
a. m
b. m
c. m
d. m
e. m
4.1 Antiderivatives and Indefinite Integration 235
4.1 Antiderivatives and Indefinite Integration
Answer Section