Exercises on Integrations
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Homework CALCULUS 1 Topic 4 MATH 1034, March 2015 Prepared by Janice WongSF 1 Homework Problem 1 (p390): The figure shows the areas of regions bounded by the graph of f and the x-axis. Evaluate the following integrals. 33. ∫ ሺሻ 34. ∫ ሺሻ 35. ∫ ሺሻ 36. ∫ ሺሻ 41. Use only the fact that ∫ ͵ሺͶ − ሻ = ͵ʹ ସ and the definitions and properties of integrals to evaluate the following integrals, if possible. a) ∫ ͵ሺͶ − ሻ ସ b) ∫ ሺ − Ͷሻ ସ c) ∫ ሺͶ − ሻ ସ d) ∫ ͵ሺͶ − ሻ 43. Suppose ∫ ሺሻ ଷ =ʹ, ∫ ሺሻ ଷ = −ͷ and ∫ ሺሻ ଷ =ͳ. Evaluate the following integrals. a) ∫ ͷሺሻ ଷ b) ∫ −͵ሺሻ ଷ c) ∫ (͵ሺሻ − ሺሻ) ଷ d) ∫ ሺሻ + ʹሺሻ ଷ Problem 2 (p404): Evaluate the following integrals. 25. ∫ ଶ −− ଷ −ଶ 27. ∫ ଶ −ͻ ହ 29. ∫ Ͷ ଷ ଶ 31. ∫ +√ ଵ 33. ∫ ଶ √ ଽ ଵ 35. ∫ ଶ −Ͷ ଶ −ଶ a b c x y=f(x) 16 11 5
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Integration
Transcript of Exercises on Integrations
Homework CALCULUS 1
Topic 4 MATH 1034, March 2015
Prepared by Janice WongSF 1
Homework
Problem 1 (p390):
The figure shows the areas of regions bounded by the graph of f and the x-axis. Evaluate the
following integrals.
33. ∫ � �
34. ∫ � �
35. ∫ � �
36. ∫ � �
41. Use only the fact that ∫ � − � � = and the definitions and properties of
integrals to evaluate the following integrals, if possible.
a) ∫ � − � �
b) ∫ � � − �
c) ∫ � − � �
d) ∫ � − � �
43. Suppose ∫ � � = , ∫ � � = − and ∫ � � = . Evaluate the following
integrals.
a) ∫ � �
b) ∫ − � �
c) ∫ ( � − � ) �
d) ∫ � + � �
Problem 2 (p404):
Evaluate the following integrals.
25. ∫ � − � −− �
27. ∫ � − �
29. ∫ � �
31. ∫ � + √� �
33. ∫ √� �
35. ∫ � −− �
a b c x
y=f(x)
16 11
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Homework CALCULUS 1
Topic 4 MATH 1034, March 2015
Prepared by Janice WongSF 2
37. ∫ �− − �
39. ∫ sec � ��
41. ∫ �− �−−
43. ∫ − � � − �
45. ∫ �
47. ∫ cos � ��8
Problem 3 (p421):
Use the given substitution to find the following indefinite integrals.
13. ∫ � � + � , = � +
15. ∫ �� � cos � �, = sin �
Find the following integrals.
17. ∫ � � − �
19. ∫ �√ − � �
21. ∫ � + � � + �
23. ∫ � � + �
27. ∫ � − � � − � �
33. ∫ �√�− �
35. ∫ �√�+ �
37. ∫ � √ � + �
Find the following definite integrals.
39. ∫ � − � �
41. ∫ sin � cos � ��
43. ∫ � � + �−
45. ∫ c s �si � ���
Problem 4 (p405): Q61 – Q67 (do only the odd)
Simplify the following expressions.
61. � ∫ + +�
63. � ∫ ���
65. � ∫ √ + �
67. � ∫ √ + �−�
