Transcription of 201-NYA-05 - Calculus 1 WORKSHEET: INTEGRALS
1 201-NYA-05 - Calculus 1 WORKSHEET: INTEGRALSE valuate the following indefinite INTEGRALS :1. (4x+ 3)dx2. (4x2 8x+ 1)dx3. (9t2 4t+ 3)dt4. (2t3 t2+ 3t 7)dt5. (1z3 3z2)dz6. (4z7 7z4+z)dz7. (3 u+1 u)du8. ( u3 12u 2+ 5)du9. (2v5/4+ 6v1/4+ 3v 4)dv10. (3v5 v5/3)dv11. (3x 1)2dx12. (x 1x)2dx13. x(2x+ 3)dx14. (2x 5)(3x+ 1)dx15. 8x 53 xdx16. 2x2 x+ 3 xdx17. x3 1x 1dx18. x3+ 3x2 9x 2x 2dx19. (t2+ 3)2t6dt20. ( t+ 2)2t3dt21. 34cosudu22. 15sinudu23. 7cscxdx24. 14 secxdx25. ( t+ cost)dt26. (3 t2 sint)dt27. sectcostdt28. 1sin2tdt29. (cscvcotvsecv)dv30. (4 + 4 tan2v)dv31. secwsinwcoswdw32. cscwcoswsinwdw33. (1 + cot2z) cotzcsczdz34. tanzcoszdz35. ddx x2+ 4dx36. ddx3 x3 8dx37. ddxsin3 xdx38. ddx x3 x x43 x2+ cos x2+ 1dxSolve the differential equation subject to the given (x) = 12x2 6x+ 1f(1) = (x) = 9x2+x 8f( 1) = 4x1/2y= 21 whenx= 4 Evaluate the following definite INTEGRALS :46.
2 102xdx47. 723dv48. 0 1(x 2)dx49. 52( 3v+ 4)dv50. 1 1(t2 2)dt51. 30(3x2+x 2)dx52. 10(2t 1)2dt53. 1 1(t3 9t)dt54. 21(3x2 1)dx55. 1 2(u 1u2)du56. 41u 2 udu57. 3 3v1/3dv58. 1 1(3 t 2)dt59. 81 2xdx60. 10x x3dx61. 20(2 t) tdt62. 0 1(t1/3 t2/3)dt63. 1 8x x223 xdx64. 30|2x 3|dx65. 40|x2 4x+ 3|dx66. 0(1 + sinx)dx67. /401 sin2 cos2 d 68. /6 /6sec2xdx69. /2 /4(2 csc2x)dx70. /3 /34 sec tan d 71. /2 /2(2t+ cost)dt72. e1(2x+1x)dx73. 51x+ 1xdx74. 20(ex+ 6)dx75. 30(t et)dt76. 1 1(e + sin )d 77. 2ee(cosx 1x)dxANSWERSI ndefinite INTEGRALS :1. 2x2+ 3x+ 4x2+x+C3. 3t3 2t2+ 3t+ t33+3t22 7t+C5. z 22+ 3z 1+C6. 4z 66+7z 33+z22+C7. 2u3/2+ 2u1/2+ +u 12+ 5u+ +24v5/45 v 3+ 3v8/38+C11. 3x3 3x2+x+ 2x x 1+ +3x22+C14. 2x3 13x22 5x+ 15x2/32+ 2x3/23+ 6x1/2+ +x22+x+ +5x22+x+C19. t 1 2t 3 9t 55+C20. t 1 8t 3/23 2t 2+ + +C23.
3 7 cosx+ + + sint+ + cost+C27. tant+C28. cott+C29. cotv+C30. 4 tanv+C31. secw+C32. cscw+C33. cscz+C34. secz+C35. x2+ 4 + x3 8 +C37. sin3 x+C38. tanx+ x x2+ 941. cotx342. cos x2+ 1 Differential (x) = 4x3 3x2+x+ (x) = 3x3+x22 8x (x) =8x3/23 13 Definite INTEGRALS :46. 147. 1548. 5249. 39250. 058. 459. 2(4 2)60. 21562. 466. + 267. 369. 2 170. 071. 4 + ln + e 177. sin(2e) sin(e) ln(2)
