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NGUYN HM V TCH PHN

I. Tm nguyn hm bng nh ngha v cc tnh cht1/ Tm nguyn hm ca cc hm s.

1. f(x) = x2 3x + S. F(x) =

2. f(x) = S. F(x) =

. f(x) = S. F(x) = lnx + + C

4. f(x) = S. F(x) =

5. f(x) = S. F(x) =

6. f(x) = S. F(x) =

7. f(x) = S. F(x) =

8. f(x) = S. F(x) =

9. f(x) = S. F(x) = x sinx + C

10. f(x) = tan2x S. F(x) = tanx x + C

11. f(x) = cos2x S. F(x) =

12. f(x) = (tanx cotx)2 S. F(x) = tanx - cotx 4x + C

13. f(x) = S. F(x) = tanx - cotx + C

14. f(x) = S. F(x) = - cotx tanx + C

15. f(x) = sin3x S. F(x) =

16. f(x) = 2sin3xcos2x S. F(x) =

17. f(x) = ex(ex 1) S. F(x) =

18. f(x) = ex(2 + S. F(x) = 2ex + tanx + C

19. f(x) = 2ax + 3x S. F(x) =

20. f(x) = e3x+1 S. F(x) =

2/ Tm hm s f(x) bit rng

1. f(x) = 2x + 1 v f(1) = 5 S. f(x) = x2 + x + 3

2. f(x) = 2 x2 v f(2) = 7/3 S. f(x) =

3. f(x) = 4 v f(4) = 0 S. f(x) =

4. f(x) = x - v f(1) = 2 S. f(x) =

5. f(x) = 4x3 3x2 + 2 v f(-1) = 3 S. f(x) = x4 x3 + 2x + 3

6. f(x) = ax + S. f(x) =

II. MT S PHNG PHP TM NGUYN HM

1.Phng php i bin s.

Tnh I = bng cch t t = u(x)

t t = u(x)

I =

BI TP

Tm nguyn hm ca cc hm s sau:

1. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

13. 14. 15. 16.

17. 18. 19. 20.

21. 22. 23. 24.

25. 26. 27. 28.

29. 30. 31. 32.

2. Phng php ly nguyn hm tng phn.

Nu u(x) , v(x) l hai hm s c o hm lin tc trn I

Hay

( vi du = u(x)dx, dv = v(x)dx)

Tm nguyn hm ca cc hm s sau:

1. 2. 3. 4

5. 6. 7. 8.

9. 10. 11. 12.

13. 14. 15. 16.

17. 18. 19. 20.

21. 22. 23. 24.

TCH PHN

I. TNH TCH PHN BNG CCH S DNG TNH CHT V NGUYN HM C BN:1.

2.

2.

3.

4.

5.

6. 7.

8. 9.

10. 11. 12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

22.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

II. PHNG PHP I BIN : 1. 2.

3. 3.

4. 5.

6. 7.

8. 9.

10. 11.

12. 13.

14. 15.

16. 17.

18. 19. 20. 21. 22.

23. 24. 25.

26. 27. 28.

29.

30. 31.

32. 33.

34.

35.

36. 37.

38. 39. 40.

41.

42.

43.

44. 45.

46.

46. 47. 48.

49. 50. 51.

52.

53.

54.

55.

56. 57.

58.

59. 60. 61. 62. 63. 64. 65.

66.

67.

68. 69.

70..

71. 72. 73.

74. 75. 76.

77.

78.

79.

80.

81. 82. 83.

84.

85.

86. 87. 88.

89. 90. 91.

92. 93.

94. 95.

96. 97. 98. 99.

100. 101.

102. 103.

104.

105.

106. 107. 108.

109.

110. 101.

112. 113.

114. 115.

116. 117.

118. 119.

120. 121. 122. 123.

124. 125. 126.

II. PHNG PHP TCH PHN TNG PHN: Cng thc tch phn tng phn :

Tich phn cac ham s d phat hin u va dv

@ Dang 1

@ Dang 2:

t

@ Dang 3:

Vi du 1: tinh cac tich phn sau

a/ t b/ t

c/

Tinh I1 bng phng phap i bin s

Tinh I2 = bng phng phap tng phn : t

Bi tp

1.

2.

3. 4.

5.

6.

7. 8.

9. 10.

11.

12.

13. 14. 15.

16.

Tnh cc tch phn sau

1) 2) 3) 4)

5) 6) 7) 8) 9) 10) 11) 12)

13)

14)

15) 16)

17) 18) 19)

20)

21) 22) 23) 24)

25) 26) 27) 28) 29) 30) 31) 32)

III. TCH PHN HM HU T:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31. 32.

33.

IV. TCH PHN HM LNG GIC:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

2.

43.

4.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66.

67.

68.

69.

70.

71.

V. TCH PHN HM V T:

Trong R(x, f(x)) c cc dng:

+) R(x, ) t x = a cos2t, t

+) R(x, ) t x = hoc x =

+) R(x, ) t t =

+) R(x, f(x)) = Vi () = k(ax+b)

Khi t t = , hoc t t =

+) R(x, ) t x = , t

+) R(x, ) t x = , t

+) R Gi k = BCNH(n1; n2; ...; ni)

t x = tk

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

VI. MT S TCH PHN C BIT:Bi ton m u: Hm s f(x) lin tc trn [-a; a], khi :

V d: +) Cho f(x) lin tc trn [-] tha mn f(x) + f(-x) = , Tnh:

+) Tnh

Bi ton 1: Hm s y = f(x) lin tc v l trn [-a, a], khi : = 0.

V d: Tnh:

Bi ton 2: Hm s y = f(x) lin tc v chn trn [-a, a], khi : = 2

V d: Tnh

Bi ton 3: Cho hm s y = f(x) lin tc, chn trn [-a, a], khi : (1b>0, a)

V d: Tnh:

Bi ton 4: Nu y = f(x) lin tc trn [0; ], th

V d: Tnh

Bi ton 5: Cho f(x) xc nh trn [-1; 1], khi :

V d: Tnh

Bi ton 6:

V d: Tnh

Bi ton 7: Nu f(x) lin tc trn R v tun hon vi chu k T th:

V d: Tnh

Cc bi tp p dng:

1.

2.

3.

4.

5.

6.

7.

8. (tga>0)

VII. TCH PHN HM GI TR TUYT I:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12. 2)

13.

14. 15.

16.

17.

18.

VIII. NG DNG CA TCH PHN:

TNH DIN TCH HNH PHNG

V d 1 : Tnh din tch hnh phng gii hn bi

a/ th hm s y = x + x -1 , trc honh , ng thng x = -2 v ng thng x = 1

b/ th hm s y = ex +1 , trc honh , ng thng x = 0 v ng thng x = 1 c/ th hm s y = x3 - 4x , trc honh , ng thng x = -2 v ng thng x = 4 d/ th hm s y = sinx , trc honh , trc tung v ng thng x = 2

V d 2 : Tnh din tch hnh phng gii hn bi

a/ th hm s y = x + x -1 , trc honh , ng thng x = -2 v ng thng x = 1

b/ th hm s y = ex +1 , trc honh , ng thng x = 0 v ng thng x = 1 c/ th hm s y = x3 - 4x , trc honh , ng thng x = -2 v ng thng x = 4 d/ th hm s y = sinx , trc honh , trc tung v ng thng x = 2

Bi 1: Cho (p) : y = x2+ 1 v ng thng (d): y = mx + 2. Tm m din tch hnh phng gii hn bi hai ng trn c din tch nh nht

Bi 2: Cho y = x4- 4x2 +m (c) Tm m hnh phng gii hn bi (c) v 0x c din tch pha trn 0x v pha di 0x bng nhau

Bi 3: Xc nh tham s m sao cho y = mx chia hnh phng gii hn bi

C hai phn din tch bng nhau

Bi 4: (p): y2=2x chia hnh phng gii bi x2+y2 = 8 thnh hai phn.Tnh din tch mi phn

Bi 5: Cho a > 0 Tnh din tch hnh phng gii hn bi Tm a din tch ln nht

Bi 6: Tnh din tch ca cc hnh phng sau:

1) (H1):

2) (H2) :

3) (H3):

4) (H4):

5) (H5):

6) (H6):

7) (H7):

8) (H8) :

9) (H9):

10) (H10): 11)

12)

13) 14) 15)

16 17 18)

19. 20): y = 4x x2 ; (p) v tip tuyn ca (p) i qua M(5/6,6)

21) 22) 23) 24)

25) 26) 27)

28)

29) 30) 31) 32) 33) 34)

35)

36) 37)

38)

39)

40) 41) 42) 43)

44) 45) 46)

47)

48)

49) 32) 33) 34)

35) 36) 37) 38) 39)

EMBED Equation.3 40) (a>0) 41) 42) 43) x2/25+y2/9 = 1 v hai tip tuyn i qua A(0;15/4)

44) Cho (p): y = x2 v im A(2;5) ng thng (d) i qua A c h s gc k .Xc nh k din tch hnh phng gii hn bi (p) v (d) nh nht

45)

TNH TH TCH VT TH TRN XOAY

Cng thc:

Bi 1: Cho min D gii hn bi hai ng : x2 + x - 5 = 0 ; x + y - 3 = 0

Tnh th tch khi trn xoay c to nn do D quay quanh trc Ox

Bi 2: Cho min D gii hn bi cc ng :

Tnh th tch khi trn xoay c to nn do D quay quanh trc Oy

Bi 3: Cho min D gii hn bi hai ng : v y = 4

Tnh th tch khi trn xoay c to nn do D quay quanh:

a) Trc Ox

b) Trc Oy

Bi 4: Cho min D gii hn bi hai ng : .


Bi 5: Cho min D gii hn bi cc ng :


Bi 6: Cho min D gii hn bi cc ng y = 2x2 v y = 2x + 4


Bi 7: Cho min D gii hn bi cc ng y = y2 = 4x v y = x


Bi 8: Cho min D gii hn bi cc ng y = ; y = 0 ; x= 1 ; x = 2


Bi 9: Cho min D gii hn bi cc ng y = xlnx ; y = 0 ; x = 1 ; x = e


Bi10: Cho min D gii hn bi cc ng y = x ; y = 0 ; x = 1


1) quay quanh trc a) 0x; b) 0y




5) quay quanh trc a) 0x;

6) (D) quay quanh trc a) 0x; ( H) nm ngoi y = x27) quay quanh trc a) 0x;

8) Min trong hnh trn (x 4)2 + y2 = 1 quay quanh trc a) 0x; b) 0y

9) Min trong (E): quay quanh trc a) 0x; b) 0y

10) quay quanh trc 0x;



13) Hnh trn tm I(2;0) bn knh R = 1 quay quanh trc a) 0x; b) 0y



EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

THI TNG KHNH THPT CAM L-QUNG TR9

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