Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

help_with_math

  • 3 years ago

Integration help! integral of sec^5 x dx

  • This Question is Closed
  1. Walleye
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    /barf im guessing u sub will help you here

  2. across
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Integration by parts!

  3. across
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Whoops, I misread.

  4. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes integration by parts

  5. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    (sec^2x)(sec^2)(sec x)

  6. across
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I read it as sec^5(x)x for a moment there. Hmm, in this case, you have to use a reduction formula.

  7. Walleye
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    red formula will work if you have it

  8. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well i havent learned taht so is tehre anoterh way to do it by parts

  9. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sec^2x = 1 + tan ^2

  10. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ( 1 + tan ^2 x ) ( 1 + tan^2 x ) (sec x )

  11. across
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I had to look it up\[\frac{\sin(x)\sec^{m-1}(x)}{m-1}+\frac{m+2}{m-1}\int\sec^{m-2}(x)dx\]

  12. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    this is wat i have so far: \[\int\limits_{}^{}\sec^3 x (\sec^2 dx)\] \[\int\limits_{}^{}\sec^3 x (1+\tan^2 x dx)\] \[\int\limits_{}^{}(\sec^3 x +\sec^3 x \tan^2 x )dx\]

  13. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    derive tan x = sec^2x

  14. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so do a u sub with u = tan x , du = sec^2 x dx

  15. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits_{}^{}(\sec^3 x) + \int\limits_{}^{}(\sec^3 x \tan^2 x) dx\] can i use u sub after this step

  16. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you will prolly end up with a ( 1 + u ) ^(to some power ) then it a simple integration

  17. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can u show me the steps after the one i just did

  18. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or wat to do?

  19. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hang on...

  20. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    im a little rusty

  21. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ughh i hate problems liek this!! XD...requires too much work

  22. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yea, it may have to be broken up into parts I cant get rid of one of the sec^x check out: http://www.wolframalpha.com/input/?i=integrate+sec^5+x

  23. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    this IS a reduction formula for powers of sec.

  24. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i did n idont understand it b.c it uses smthng i didnt leard which is teh reduction formula thing

  25. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then again do u mind tellin me wat that is

  26. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or how to use it

  27. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yea, your instructor may not accept a reduction formula answer, it the quick way, but there is a trigonometric solution for this.

  28. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cool i will prob understand that if u explain

  29. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the trig solution i mean

  30. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    there is an identity that will lead to an integral of u. anywa here is a like with the reduction formula for secant, and others http://www.sosmath.com/calculus/integration/moretrigpower/moretrigpower.html

  31. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    as a matter of fact I bet your textbook has a table of integrals for integrals of powers of secant

  32. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what is the dffnce between sex^n (x) and sec^n (ax)

  33. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    a=1

  34. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i wud use the first formula right? sec^5 (x) = sec ^5-2 (x) sec^2(x) = sec^3 (tan^2 x * sec^2 x -1)

  35. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    where do u go on from there

  36. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    omg i havent done definite integrals!

  37. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no, I mistyped

  38. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ∫sec^5dx=1/4sec^3xtanx+3/4∫sec^3xdx

  39. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no definite integrals here

  40. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm how did u get 1/4 sec ...etc

  41. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    then apply the reduction formula ( or integrate ) \[\int\limits \sec ^ 3 x dx\]

  42. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im confused how u got the previous step thou

  43. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    its from the reduction formula, it ends with an integral of ∫sec^3xdx

  44. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i mean teh 1/4 sec part im confused about

  45. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    in the reduction formula it 1/(a(n-1) n=5, the power of secant a = 1

  46. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so now how did u get 3/4?

  47. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    from the reduction formula: (n-2)/(n-1) again n = 5, the power of the secant

  48. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you instructor will be either impressed or put off that you are using the integral tables. :)

  49. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol...he will b impressed hopefully...i have a test 2mm n im trying to udnerstand probs idk

  50. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yea the trigonometric integrals take practice( obviously )

  51. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    srry this is new to me so after taht step wat do u do..u still have a integral of sec^3 dx to deal with

  52. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    right! so integrate the sec^x or use the formula again, but this time with n = 3, see?

  53. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sec^x is short, but it indefinite integral has many parts.

  54. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so after using n=3 do u get 1/2 sec x dx

  55. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    right ( n-2)/(n-1) this time the formula will end with \[\int\limits \sec x dx\]

  56. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wait but isnt is half secant

  57. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so how is teh integral jsut sec

  58. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no the formula will end ith ∫secxdx, integrate that and you are done.

  59. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\int\limits \sec x dx = \ln ( \sec x +tanx ) + C\]

  60. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so teh final answer is: 1/4 sec^3 x tanx + 3/4 ...idk teh rest

  61. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    1/4 sec^3 x tanx + 3/4∫sec^3xdx then apply the formula again for ∫sec^3xdx that answer will end with ∫sec xdx integrate ∫secxdx, done!

  62. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so the final asnwer is: 1/4 sec^3 x tanx + 3/8 sec x tanx + tn (secx+tanx) + C

  63. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    SRY TAHTS SUPPOOSED TO be ln not tn

  64. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    right, distribute the 3/4, I didnt work it all out but it looks right. Those tables are in you textbook right, in the appendix?

  65. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    let me check now

  66. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    "table of integrals"

  67. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    under wat heading shud i looj for te hreduction formulas

  68. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i see basic forms, forms invlving sqrt of (a^2+u^2, forms involving (a^2 - u^2), forms involvung sqrt of (u^2 - a^2), forms involving a+bu, trig forms, inverse trig forms, exp and log forms, hyperbolic forms

  69. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Tables of integrals, Lists of Integrals usually in the appendix, could be on the inside covers.

  70. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i see them in the appenxix...jsut under wat heading of integrals will i fimd teh reduction formulas

  71. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or wher u jsut letting me know taht tehre was a table of integrtals

  72. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that really what we were using, an integration formula, so you can integrate by parts or look up the formula.

  73. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    there might be one for ∫sec^n (ax)dx

  74. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    might not http://integral-table.com/

  75. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ths is wat is in my bk...sec^n du = 1/n tan u sec^n-2 + (n-2/n-1) *integral of sec^n-2 u du

  76. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i guess tahts anoterh form of te one u showed me

  77. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    right that one dont account for a coefficient on x. so, yea, you seem to have it. Im out. ( gotta brush up on my integrals ;) )

  78. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    THANK U SOOOOO MUCH!!! PLUS THE WEBSITE LOOKS SUPER HELPFUL =)

  79. Roachie
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    peace

  80. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ii imma go study sum more

  81. help_with_math
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    gnite

  82. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.