Bai Tap Tich Phan Tong Hop

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<p>WWW.ToanCapBa.Net</p> <p>NGUYN HM V TCH PHN </p> <p>I. Tm nguyn hm bng nh ngha v cc tnh cht1/ Tm nguyn hm ca cc hm s.</p> <p>1. f(x) = x2 3x + S. F(x) = </p> <p>2. f(x) = S. F(x) = </p> <p>. f(x) = S. F(x) = lnx + + C </p> <p>4. f(x) = S. F(x) = </p> <p>5. f(x) = S. F(x) = </p> <p>6. f(x) = S. F(x) = </p> <p>7. f(x) = S. F(x) = </p> <p>8. f(x) = S. F(x) = </p> <p>9. f(x) = S. F(x) = x sinx + C </p> <p>10. f(x) = tan2x S. F(x) = tanx x + C </p> <p>11. f(x) = cos2x S. F(x) = </p> <p>12. f(x) = (tanx cotx)2 S. F(x) = tanx - cotx 4x + C</p> <p>13. f(x) = S. F(x) = tanx - cotx + C </p> <p>14. f(x) = S. F(x) = - cotx tanx + C </p> <p>15. f(x) = sin3x S. F(x) = </p> <p>16. f(x) = 2sin3xcos2x S. F(x) = </p> <p>17. f(x) = ex(ex 1) S. F(x) = </p> <p>18. f(x) = ex(2 + S. F(x) = 2ex + tanx + C </p> <p>19. f(x) = 2ax + 3x S. F(x) = </p> <p>20. f(x) = e3x+1 S. F(x) = </p> <p>2/ Tm hm s f(x) bit rng </p> <p>1. f(x) = 2x + 1 v f(1) = 5 S. f(x) = x2 + x + 3 </p> <p>2. f(x) = 2 x2 v f(2) = 7/3 S. f(x) = </p> <p>3. f(x) = 4 v f(4) = 0 S. f(x) = </p> <p>4. f(x) = x - v f(1) = 2 S. f(x) = </p> <p>5. f(x) = 4x3 3x2 + 2 v f(-1) = 3 S. f(x) = x4 x3 + 2x + 3</p> <p>6. f(x) = ax + S. f(x) = </p> <p>II. MT S PHNG PHP TM NGUYN HM</p> <p>1.Phng php i bin s.</p> <p>Tnh I = bng cch t t = u(x)</p> <p> t t = u(x)</p> <p> I = </p> <p>BI TP</p> <p>Tm nguyn hm ca cc hm s sau:</p> <p>1. 2. 3. 4. </p> <p>5. 6. 7. 8. </p> <p>9. 10. 11. 12. </p> <p>13. 14. 15. 16. </p> <p>17. 18. 19. 20. </p> <p>21. 22. 23. 24. </p> <p>25. 26. 27. 28. </p> <p>29. 30. 31. 32. </p> <p>2. Phng php ly nguyn hm tng phn.</p> <p>Nu u(x) , v(x) l hai hm s c o hm lin tc trn I</p> <p>Hay</p> <p> ( vi du = u(x)dx, dv = v(x)dx)</p> <p>Tm nguyn hm ca cc hm s sau:</p> <p>1. 2. 3. 4</p> <p>5. 6. 7. 8. </p> <p>9. 10. 11. 12. </p> <p>13. 14. 15. 16. </p> <p>17. 18. 19. 20. </p> <p>21. 22. 23. 24. </p> <p>TCH PHN</p> <p>I. TNH TCH PHN BNG CCH S DNG TNH CHT V NGUYN HM C BN:1.</p> <p>2. </p> <p> 2. </p> <p>3. </p> <p> 4. </p> <p>5. </p> <p>6. 7. </p> <p> 8. 9. </p> <p>10. 11. 12. </p> <p>13. </p> <p>14. </p> <p>15. </p> <p>16. </p> <p>17. </p> <p>18. </p> <p>19. </p> <p>20. </p> <p>21. </p> <p>22. </p> <p>22. </p> <p>24. </p> <p>25. </p> <p>26. </p> <p>27. </p> <p>28. </p> <p>29. </p> <p>30. </p> <p>31. </p> <p>32. </p> <p>33. </p> <p>II. PHNG PHP I BIN : 1. 2. </p> <p>3. 3. </p> <p>4. 5. </p> <p> 6. 7. </p> <p> 8. 9. </p> <p> 10. 11. </p> <p>12. 13. </p> <p>14. 15. </p> <p> 16. 17. </p> <p> 18. 19. 20. 21. 22. </p> <p>23. 24. 25. </p> <p>26. 27. 28. </p> <p>29. </p> <p>30. 31. </p> <p>32. 33. </p> <p>34. </p> <p>35. </p> <p>36. 37. </p> <p> 38. 39. 40. </p> <p> 41. </p> <p>42. </p> <p>43. </p> <p> 44. 45. </p> <p>46. </p> <p>46. 47. 48. </p> <p> 49. 50. 51. </p> <p>52. </p> <p>53. </p> <p>54. </p> <p>55. </p> <p>56. 57. </p> <p>58. </p> <p>59. 60. 61. 62. 63. 64. 65. </p> <p>66.</p> <p> 67. </p> <p>68. 69. </p> <p>70.. </p> <p>71. 72. 73. </p> <p>74. 75. 76. </p> <p>77. </p> <p>78. </p> <p>79. </p> <p>80. </p> <p>81. 82. 83. </p> <p>84. </p> <p>85. </p> <p>86. 87. 88. </p> <p>89. 90. 91. </p> <p>92. 93. </p> <p>94. 95. </p> <p>96. 97. 98. 99. </p> <p>100. 101. </p> <p>102. 103. </p> <p>104. </p> <p> 105. </p> <p>106. 107. 108. </p> <p>109. </p> <p>110. 101. </p> <p>112. 113. </p> <p>114. 115. </p> <p>116. 117. </p> <p>118. 119. </p> <p>120. 121. 122. 123. </p> <p>124. 125. 126. </p> <p>II. PHNG PHP TCH PHN TNG PHN: Cng thc tch phn tng phn : </p> <p> Tich phn cac ham s d phat hin u va dv</p> <p> @ Dang 1 </p> <p> @ Dang 2: </p> <p> t </p> <p>@ Dang 3: </p> <p>Vi du 1: tinh cac tich phn sau</p> <p> a/ t b/ t </p> <p> c/</p> <p> Tinh I1 bng phng phap i bin s</p> <p>Tinh I2 = bng phng phap tng phn : t </p> <p>Bi tp</p> <p>1. </p> <p>2. </p> <p>3. 4. </p> <p> 5. </p> <p>6. </p> <p> 7. 8. </p> <p>9. 10. </p> <p> 11. </p> <p>12. </p> <p> 13. 14. 15. </p> <p>16. </p> <p>Tnh cc tch phn sau </p> <p>1) 2) 3) 4) </p> <p> 5) 6) 7) 8) 9) 10) 11) 12) </p> <p> 13) </p> <p> 14) </p> <p> 15) 16) </p> <p> 17) 18) 19) </p> <p> 20) </p> <p> 21) 22) 23) 24) </p> <p>25) 26) 27) 28) 29) 30) 31) 32) </p> <p>III. TCH PHN HM HU T:</p> <p>1. </p> <p>2. </p> <p>3. </p> <p>4. </p> <p>5. </p> <p>6. </p> <p>7. </p> <p>8. </p> <p>9. </p> <p>10. </p> <p>11. </p> <p>12. </p> <p>13. </p> <p>14. </p> <p>15. </p> <p>16. </p> <p>17. </p> <p>18. </p> <p>19. </p> <p>20. </p> <p>21. </p> <p>22. </p> <p>23. </p> <p>24. </p> <p>25. </p> <p>26. </p> <p>27. </p> <p>28. </p> <p>29. </p> <p>30. </p> <p>31. 32. </p> <p>33. </p> <p>IV. TCH PHN HM LNG GIC:</p> <p>1. </p> <p>2. </p> <p>3. </p> <p>4. </p> <p>5. </p> <p>6. </p> <p>7. </p> <p>8. </p> <p>9. </p> <p>10. </p> <p>11. </p> <p>12. </p> <p>13. </p> <p>14. </p> <p>15. </p> <p>16. </p> <p>17. </p> <p>18. </p> <p>19. </p> <p>20. </p> <p>21. </p> <p>22. </p> <p>23. </p> <p>24. </p> <p>25. </p> <p>26. </p> <p>27. </p> <p>28. </p> <p>29. </p> <p>30. </p> <p>31. </p> <p>32. </p> <p>33. </p> <p>34. </p> <p>35. </p> <p>36. </p> <p>37. </p> <p>38. </p> <p>39. </p> <p>40. </p> <p>41. </p> <p>2. </p> <p>43. </p> <p>4. </p> <p>45. </p> <p>46. </p> <p>47. </p> <p>48. </p> <p>49. </p> <p>50. </p> <p>51. </p> <p>52. </p> <p>53. </p> <p>54. </p> <p>55. </p> <p>56. </p> <p>57. </p> <p>58. </p> <p>59. </p> <p>60. </p> <p>61. </p> <p>62. </p> <p>63. </p> <p>64. </p> <p>65. </p> <p>66. </p> <p>67. </p> <p>68. </p> <p>69. </p> <p>70. </p> <p>71. </p> <p>V. TCH PHN HM V T:</p> <p>Trong R(x, f(x)) c cc dng: </p> <p>+) R(x, ) t x = a cos2t, t </p> <p>+) R(x, ) t x = hoc x = </p> <p>+) R(x, ) t t = </p> <p>+) R(x, f(x)) = Vi () = k(ax+b)</p> <p>Khi t t = , hoc t t = </p> <p>+) R(x, ) t x = , t </p> <p>+) R(x, ) t x = , t</p> <p>+) R Gi k = BCNH(n1; n2; ...; ni) </p> <p>t x = tk </p> <p>1. </p> <p>2. </p> <p>3. </p> <p>4. </p> <p>5. </p> <p>6. </p> <p>7. </p> <p>8. </p> <p>9. </p> <p>10. </p> <p>11. </p> <p>12. </p> <p>13. </p> <p>14. </p> <p>15. </p> <p>16. </p> <p>17. </p> <p>18. </p> <p>19. </p> <p>20. </p> <p>21. </p> <p>22. </p> <p>23. </p> <p>24. </p> <p>25. </p> <p>26. </p> <p>27. </p> <p>28. </p> <p>29. </p> <p>30.</p> <p>31. </p> <p>32. </p> <p>33. </p> <p>34. </p> <p>35. </p> <p>36. </p> <p>37. </p> <p>38. </p> <p>39. </p> <p>40. </p> <p>VI. MT S TCH PHN C BIT:Bi ton m u: Hm s f(x) lin tc trn [-a; a], khi : </p> <p>V d: +) Cho f(x) lin tc trn [-] tha mn f(x) + f(-x) = , Tnh: </p> <p>+) Tnh </p> <p>Bi ton 1: Hm s y = f(x) lin tc v l trn [-a, a], khi : = 0.</p> <p>V d: Tnh:</p> <p>Bi ton 2: Hm s y = f(x) lin tc v chn trn [-a, a], khi : = 2</p> <p>V d: Tnh </p> <p>Bi ton 3: Cho hm s y = f(x) lin tc, chn trn [-a, a], khi : (1b&gt;0, a)</p> <p>V d: Tnh: </p> <p>Bi ton 4: Nu y = f(x) lin tc trn [0; ], th </p> <p>V d: Tnh </p> <p>Bi ton 5: Cho f(x) xc nh trn [-1; 1], khi : </p> <p>V d: Tnh</p> <p>Bi ton 6: </p> <p>V d: Tnh </p> <p>Bi ton 7: Nu f(x) lin tc trn R v tun hon vi chu k T th: </p> <p>V d: Tnh</p> <p>Cc bi tp p dng:</p> <p>1. </p> <p>2. </p> <p>3. </p> <p>4. </p> <p>5. </p> <p>6.</p> <p>7. </p> <p>8. (tga&gt;0)</p> <p>VII. TCH PHN HM GI TR TUYT I:</p> <p>1. </p> <p>2. </p> <p>3.</p> <p>4. </p> <p>5. </p> <p>6. </p> <p>7. </p> <p>8. </p> <p>9. </p> <p>10. </p> <p>11. </p> <p>12. 2) </p> <p>13. </p> <p>14. 15. </p> <p>16. </p> <p>17. </p> <p>18. </p> <p>VIII. NG DNG CA TCH PHN:</p> <p>TNH DIN TCH HNH PHNG</p> <p>V d 1 : Tnh din tch hnh phng gii hn bi </p> <p> a/ th hm s y = x + x -1 , trc honh , ng thng x = -2 v ng thng x = 1</p> <p> 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</p> <p>V d 2 : Tnh din tch hnh phng gii hn bi </p> <p> a/ th hm s y = x + x -1 , trc honh , ng thng x = -2 v ng thng x = 1</p> <p> 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</p> <p>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</p> <p>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</p> <p>Bi 3: Xc nh tham s m sao cho y = mx chia hnh phng gii hn bi </p> <p>C hai phn din tch bng nhau</p> <p>Bi 4: (p): y2=2x chia hnh phng gii bi x2+y2 = 8 thnh hai phn.Tnh din tch mi phn</p> <p>Bi 5: Cho a &gt; 0 Tnh din tch hnh phng gii hn bi Tm a din tch ln nht</p> <p>Bi 6: Tnh din tch ca cc hnh phng sau:</p> <p>1) (H1):</p> <p>2) (H2) : </p> <p>3) (H3):</p> <p>4) (H4):</p> <p>5) (H5):</p> <p>6) (H6):</p> <p>7) (H7):</p> <p> 8) (H8) : </p> <p>9) (H9): </p> <p>10) (H10): 11) </p> <p>12) </p> <p>13) 14) 15) </p> <p>16 17 18) </p> <p>19. 20): y = 4x x2 ; (p) v tip tuyn ca (p) i qua M(5/6,6)</p> <p>21) 22) 23) 24) </p> <p>25) 26) 27) </p> <p>28)</p> <p>29) 30) 31) 32) 33) 34) </p> <p>35) </p> <p>36) 37) </p> <p>38)</p> <p>39)</p> <p>40) 41) 42) 43) </p> <p>44) 45) 46) </p> <p>47) </p> <p>48) </p> <p>49) 32) 33) 34) </p> <p>35) 36) 37) 38) 39)</p> <p> EMBED Equation.3 40) (a&gt;0) 41) 42) 43) x2/25+y2/9 = 1 v hai tip tuyn i qua A(0;15/4)</p> <p>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</p> <p>45) </p> <p>TNH TH TCH VT TH TRN XOAY</p> <p> Cng thc:</p> <p>Bi 1: Cho min D gii hn bi hai ng : x2 + x - 5 = 0 ; x + y - 3 = 0</p> <p>Tnh th tch khi trn xoay c to nn do D quay quanh trc Ox</p> <p>Bi 2: Cho min D gii hn bi cc ng : </p> <p>Tnh th tch khi trn xoay c to nn do D quay quanh trc Oy</p> <p>Bi 3: Cho min D gii hn bi hai ng : v y = 4</p> <p>Tnh th tch khi trn xoay c to nn do D quay quanh:</p> <p>a) Trc Ox</p> <p>b) Trc Oy</p> <p>Bi 4: Cho min D gii hn bi hai ng : .</p> <p>Tnh th tch khi trn xoay c to nn do D quay quanh trc Ox</p> <p>Bi 5: Cho min D gii hn bi cc ng : </p> <p>Tnh th tch khi trn xoay c to nn do D quay quanh trc Ox</p> <p>Bi 6: Cho min D gii hn bi cc ng y = 2x2 v y = 2x + 4</p> <p> Tnh th tch khi trn xoay c to nn do D quay quanh trc Ox</p> <p>Bi 7: Cho min D gii hn bi cc ng y = y2 = 4x v y = x</p> <p> Tnh th tch khi trn xoay c to nn do D quay quanh trc Ox</p> <p>Bi 8: Cho min D gii hn bi cc ng y = ; y = 0 ; x= 1 ; x = 2</p> <p> Tnh th tch khi trn xoay c to nn do D quay quanh trc Ox</p> <p>Bi 9: Cho min D gii hn bi cc ng y = xlnx ; y = 0 ; x = 1 ; x = e</p> <p> Tnh th tch khi trn xoay c to nn do D quay quanh trc Ox</p> <p>Bi10: Cho min D gii hn bi cc ng y = x ; y = 0 ; x = 1</p> <p> Tnh th tch khi trn xoay c to nn do D quay quanh trc Ox</p> <p>1) quay quanh trc a) 0x; b) 0y</p> <p>2) quay quanh trc a) 0x; b) 0y</p> <p>3) quay quanh trc a) 0x; b) 0y</p> <p>4) quay quanh trc a) 0x; b) 0y</p> <p>5) quay quanh trc a) 0x; </p> <p>6) (D) quay quanh trc a) 0x; ( H) nm ngoi y = x27) quay quanh trc a) 0x; </p> <p>8) Min trong hnh trn (x 4)2 + y2 = 1 quay quanh trc a) 0x; b) 0y</p> <p>9) Min trong (E): quay quanh trc a) 0x; b) 0y</p> <p>10) quay quanh trc 0x;</p> <p>11) quay quanh trc 0x;</p> <p>12) quay quanh trc 0x;</p> <p>13) Hnh trn tm I(2;0) bn knh R = 1 quay quanh trc a) 0x; b) 0y</p> <p>14) quay quanh trc 0x;</p> <p>15) quay quanh trc a) 0x; b) 0y</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>EMBED Equation.3</p> <p>THI TNG KHNH THPT CAM L-QUNG TR9</p> <p>_1290818293.unknown</p> <p>_1290819144.unknown</p> <p>_1290819194.unknown</p> <p>_1290968115.unknown</p> <p>_1291646746.unknown</p> <p>_1291647426.unknown</p> <p>_1291647696.unknown</p> <p>_1291648867.unknown</p> <p>_1413028710.unknown</p> <p>_1291649368.unknown</p> <p>_1291648865.unknown</p> <p>_1291648866.unknown</p> <p>_1291647716.unknown</p> <p>_1291647455.unknown</p> <p>_1291647456.unknown</p> <p>_1291647453.unknown</p> <p>_1291647241.unknown</p> <p>_1291647340.unknown</p> <p>_1291647370.unknown</p> <p>_1291647278.unknown</p> <p>_1291647207.unknown</p> <p>_1291647231.unknown</p> <p>_1291647205.unknown</p> <p>_1290969258.unknown</p> <p>_1290972047.unknown</p> <p>_1291026731.unknown</p> <p>_1291027380.unknown</p> <p>_1291029023.unknown</p> <p>_1291029357.unknown</p> <p>_1291479785.unknown</p> <p>_1291029129.unknown</p> <p>_1291028187.unknown</p> <p>_1291028356.unknown</p> <p>_1291028462.unknown</p> <p>_1291027503.unknown</p> <p>_1291026937.unknown</p> <p>_129102...</p>