351 Chapter 5: Integration
____ 7. Find the indefinite integral .
a.
b.
c.
d.
e.
____ 8. Find .
a.
b.
c.
d.
e.
____ 9. Find .
a.
b.
c.
d.
e.
5.7 The natural Lodarithmic Function: Integration
352
____ 10. Find the indefinite integral.
.
a.
b.
c.
d.
e.
____ 11. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 12. Find the solution of the differential equation which passes through the point
.
a.
b.
c.
d.
e.
353
Chapter 5: Integration
____
13.
Find the solution of the differential equation
which passes through the
point
.
a.
b.
c.
d.
e.
____ 14. Use integration to find the particular solution of the differential equation which
passes through the point .
a.
b.
c.
d.
e.
____ 15. Evaluate .
a.
b.
c.
d.
e.
5.7 The natural Lodarithmic Function: Integration
354
____ 16. Evaluate the definite integral .
a.
b.
c.
d.
e.
____ 17. Evaluate the definite integral.
a.
b.
c.
d.
e.
____ 18. Find .
a.
b.
c.
355 Chapter 5: Integration
d.
e.
____ 19. Find given .
a.
b.
c.
d.
e.
____ 20. Find if .
a.
b.
c.
d.
e.
5.7 The natural Lodarithmic Function: Integration
356
____ 21.
.
a.
b.
c.
d.
e.
____ 22. Find the area of the region bounded by the graphs of the equations
Round your answer to four decimal places.
7.2189
7.5835
8.2189
8.5835
8.8283
____ 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 500. Write an equation that gives the
population at any time t.
a.
b.
c.
d.
e.
357 Chapter 5: Integration
____ 24. 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.
12,783
11,525
13,533
10,772
11,522
____ 25. 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.
6.4346 minutes
4.4251 minutes
3.6907 minutes
4.0598 minutes
5.8496 minutes
____ 26. Suppose the demand equation for a product is Find the average price p on the interval
. Round your answer to the nearest dollar.
$67
$83
$57
$565
$52
____ 27. The rate of change in sales S is inversely proportional to time measured in weeks.
Find S as a function of t if sales after 2 and 4 weeks are 200 units and 350 units respectively.
a.
b.
c.
d.
e.
5.7 The natural Lodarithmic Function: Integration
358
5.7 The Natural Logarithmic Function: Integration
Answer Section
359
Chapter 5: Integration
24.
25.
27.
5.8 Inverse Trigonometric Functions: Integration
360
5.8 Inverse Trigonometric Functions: Integration
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 2. Find the indefinite integral.
a.
b.
c.
d.
e.
361 Chapter 5: Integration
____ 3. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 4. Find the integral
a.
b.
c.
d.
e.
5.8 Inverse Trigonometric Functions: Integration
362
____
5.
Find the integral
a.
b.
c.
d.
e.
____
6.
Find the integral
a.
b.
c.
d.
e.
363 Chapter 5: Integration
____
7.
Find the integral
a.
b.
c.
d.
e.
____
8.
Evaluate the integral
a.
b.
c.
d.
e.
____
9.
Evaluate the integral
a.
b.
c.
d.
e.
5.8 Inverse Trigonometric Functions: Integration
364
____ 10. Find the indefinite integral.
a.
b.
c.
d.
e.
____ 11. Find the indefinite integral.
a.
b.
c.
d.
e.
365
Chapter 5: Integration
____
12.
Use the differential equation
and the initial condition
to
find y.
a.
b.
c.
d.
e.
____
13.
Use the differential equation
and the initial condition
to
find y.
a.
b.
c.
d.
e.
____ 14. Find the area of the shaded region for the function .
5.8 Inverse Trigonometric Functions: Integration
366
a.
b.
c.
d.
e.
____ 15. Find the area of the shaded region for the function .
a.
b.
c.
d.
e.
367
Chapter 5: Integration
____
16.
Find the area of the shaded region for the function
.
a.
b.
c.
d.
e.
5.8 Inverse Trigonometric Functions: Integration
368
5.8 Inverse Trigonometric Functions: Integration
Answer Section