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292 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
5.2 The Natural Logarithmic Function: Integration
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the indefinite integral of .
a.
b.
c.
d.
e.
____ 2. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 3. Find the indefinite integral .
a.
b.
c.
d.
e.
5.2 The Natural Logarithmic Function: Integration 293
____ 4. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 5. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 6. Find .
a.
b.
c.
d.
e.
294 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
____ 7. Find the indefinite integral .
a.
b.
c.
d.
e.
____ 8. Find .
a.
b.
c.
d.
e.
____ 9. Find .
a.
b.
c.
d.
e.
5.2 The Natural Logarithmic Function: Integration 295
____ 10. Find the indefinite integral.
.
a.
b.
c.
d.
e.
____ 11. Find the solution of the differential equation which passes through the
point .
a.
b.
c.
d.
e.
____ 12. Find the solution of the differential equation which passes through the
point .
a.
b.
c.
d.
e.
____ 13. Use integration to find the particular solution of the differential equation
which passes through the point .
a.
b.
296 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
c.
d.
e.
____ 14. Evaluate .
a.
b.
c.
d.
e.
____ 15. Evaluate the definite integral .
a.
b.
c.
d.
e.
____ 16. Evaluate the definite integral.
5.2 The Natural Logarithmic Function: Integration 297
a.
b.
c.
d.
e.
____ 17. Find .
a.
b.
c.
d.
e.
____ 18. Find given .
a.
b.
c.
d.
e.
298 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
____ 19. Find if .
a.
b.
c.
d.
e.
____ 20. Find the area of the region given below bounded by the graph of .
a.
b.
c.
d.
e.
____ 21. Find the area of the region bounded by the graphs of the equations
Round your answer to four decimal places.
a. 13.6566
b. 12.3178
c. 12.6566
d. 11.3178
e. 12.7041
5.2 The Natural Logarithmic Function: Integration 299
____ 22. Suppose a population of bacteria is changing at a rate of where t is the
time in days. The initial population (when t = 0) is 500. Write an equation that gives the population at
any time t.
a.
b.
c.
d.
e.
____ 23. Suppose a population of bacteria is changing at a rate of where t is the
time in days. The initial population (when t = 0) is 1,500. Identify an equation that gives the
population at any time t and use it to find the population when days. Round your answer to the
nearest integer.
a. 12,783
b. 11,525
c. 13,533
d. 10,772
e. 11,522
____ 24. Find the time required for an object to cool from by evaluating
, where t is time in minutes. Round your answer to four decimal places.
a. 6.4346 minutes
b. 4.4251 minutes
c. 3.6907 minutes
d. 4.0598 minutes
e. 5.8496 minutes
____ 25. Suppose the demand equation for a product is Find the average price p
on the interval . Round your answer to the nearest dollar.
a. $67
b. $83
c. $57
d. $565
e. $52
300 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions
5.2 The Natural Logarithmic Function: Integration
Answer Section
5.2 The Natural Logarithmic Function: Integration 301
