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roselin

  • 2 years ago

evaluate indefinite integrals intergral tan^2x Sec^2x dx

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  1. cinar
    • 2 years ago
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    tanx=u

  2. cinar
    • 2 years ago
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    take the derivative

  3. roselin
    • 2 years ago
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    derivative of tanx?

  4. cinar
    • 2 years ago
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    both sides

  5. cinar
    • 2 years ago
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    what is it

  6. roselin
    • 2 years ago
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    derivative of tna is sec^2x

  7. cinar
    • 2 years ago
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    sec^2xdx=du

  8. cinar
    • 2 years ago
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    subs. them in int.

  9. cinar
    • 2 years ago
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    if tanx=u then what is tan^2x

  10. roselin
    • 2 years ago
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    u sqre

  11. cinar
    • 2 years ago
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    good

  12. cinar
    • 2 years ago
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    then what is your new int. depends on only u

  13. cinar
    • 2 years ago
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    int. tan^2x Sec^2x dx sec^2xdx=du tan^2x=u^2

  14. roselin
    • 2 years ago
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    csc x^3/ 3 ?

  15. cinar
    • 2 years ago
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    |dw:1355646302656:dw|

  16. cinar
    • 2 years ago
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    what are they in u

  17. roselin
    • 2 years ago
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    u^2 . du

  18. cinar
    • 2 years ago
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    yesssssss..

  19. cinar
    • 2 years ago
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    solve that integral..

  20. roselin
    • 2 years ago
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    1/3 tan^3 x+c ?

  21. cinar
    • 2 years ago
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    you got it..

  22. roselin
    • 2 years ago
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    but i have one question though

  23. cinar
    • 2 years ago
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    shoot it..

  24. roselin
    • 2 years ago
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    |dw:1355639354738:dw|

  25. cinar
    • 2 years ago
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    |dw:1355646949637:dw|

  26. roselin
    • 2 years ago
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    did not get it,s orry

  27. cinar
    • 2 years ago
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    they are the same thing but just different letter..

  28. cinar
    • 2 years ago
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    |dw:1355647192985:dw|

  29. roselin
    • 2 years ago
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    oh okay.

  30. cinar
    • 2 years ago
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    dx or du they are just saying that you are taking int. depends on that variable

  31. cinar
    • 2 years ago
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    |dw:1355647315134:dw|

  32. cinar
    • 2 years ago
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    you can assume that x is just a constant in here..

  33. roselin
    • 2 years ago
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    okay,thanks. i have another problem, will you help me with that?

  34. cinar
    • 2 years ago
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    ok..

  35. roselin
    • 2 years ago
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    thanks

  36. roselin
    • 2 years ago
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    |dw:1355640103615:dw|

  37. cinar
    • 2 years ago
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    |dw:1355647649309:dw|

  38. cinar
    • 2 years ago
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    take derivative

  39. roselin
    • 2 years ago
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    how do you decide which one is "U"?

  40. cinar
    • 2 years ago
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    (:

  41. cinar
    • 2 years ago
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    because I can see that derivative sinx =cosxdx and it is above

  42. cinar
    • 2 years ago
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    |dw:1355647787810:dw|

  43. roselin
    • 2 years ago
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    derivative of sin theta = cos theta d theta

  44. cinar
    • 2 years ago
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    but it is sinsqrt theta

  45. roselin
    • 2 years ago
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    cos sqrt theta d theta

  46. cinar
    • 2 years ago
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    |dw:1355647993776:dw|

  47. cinar
    • 2 years ago
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    one more thing youre missing

  48. roselin
    • 2 years ago
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    what is it?

  49. cinar
    • 2 years ago
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    derivative of sqrt theta

  50. roselin
    • 2 years ago
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    |dw:1355640793032:dw|

  51. cinar
    • 2 years ago
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    |dw:1355648238516:dw|

  52. cinar
    • 2 years ago
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    |dw:1355648283456:dw|

  53. roselin
    • 2 years ago
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    how did you get that half?

  54. cinar
    • 2 years ago
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    |dw:1355648328997:dw|

  55. cinar
    • 2 years ago
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    |dw:1355648354029:dw|

  56. cinar
    • 2 years ago
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    |dw:1355648407558:dw|

  57. cinar
    • 2 years ago
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    what is your new integral..

  58. cinar
    • 2 years ago
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    |dw:1355648571843:dw|

  59. roselin
    • 2 years ago
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    1/2 integral 1/sin sqrt theta +c?

  60. cinar
    • 2 years ago
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    |dw:1355648717143:dw|

  61. cinar
    • 2 years ago
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    |dw:1355648783325:dw|

  62. roselin
    • 2 years ago
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    confused

  63. cinar
    • 2 years ago
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    what is int. 1/x dx=?

  64. roselin
    • 2 years ago
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    d

  65. roselin
    • 2 years ago
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    x

  66. cinar
    • 2 years ago
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    |dw:1355648969297:dw|

  67. roselin
    • 2 years ago
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    okay

  68. cinar
    • 2 years ago
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    in your case lnu+c put u back in

  69. cinar
    • 2 years ago
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    I gotta go, any question..

  70. roselin
    • 2 years ago
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    so,thats the ans ? after putting the u?

  71. cinar
    • 2 years ago
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    yes, ln(sin sqrt theta)+c is the answer..

  72. roselin
    • 2 years ago
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    okay,thanks a lot

  73. cinar
    • 2 years ago
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    np..

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