1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integration problem using substitution

  1. Feb 1, 2017 #1
    1. The problem statement, all variables and given/known data

    using ## u= sin 4x## find the exact value of ##∫ (cos^3 4x) dx##



    2. Relevant equations


    3. The attempt at a solution

    ## u= sin 4x##
    on integration ##u^2/2=-cos4x/4 ## , →##-2u^6={cos 4x}^3 ##......am i on the right track because now i end up with ##∫{{-2u^6}/{4.-2u^2}}du## or should i use

    ##du=4cos 4x dx ## to end up with ## 0.25 ∫ cos^24x du## which looks wrong to me
     
  2. jcsd
  3. Feb 1, 2017 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    No, you've integrated one side wrt u and the other wrt x.
     
  4. Feb 1, 2017 #3
    so should i use the second approach?
     
  5. Feb 1, 2017 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yes, but you need to get all of the references to x turned into references to u.

    You are asked for an exact value, but it is an indefinite integral. Remember that the limits need to be expressed in terms of u as well.
     
  6. Feb 1, 2017 #5
    yes the limits are from 0 to π/24
     
  7. Feb 1, 2017 #6
    is ## 0.25∫{cos^24x}du## correct?
     
  8. Feb 1, 2017 #7

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    So what are the limits on u?
    Yes.
     
  9. Feb 1, 2017 #8
    limits on u are 0 to 30, now how do i proceed with the integration?
     
  10. Feb 1, 2017 #9
    ## cos^2 4x## = ##(cos 8x+1)##/2

    should we substitute again? or are we going to have


    ##0.25∫cos^24x d {sin4x} ##
     
  11. Feb 1, 2017 #10
    i am a bit confused we cannot integrate a variable say ##x## with respect to another variable say ##u##, i am stuck here
     
  12. Feb 1, 2017 #11

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    No.
    You have the cos2 of some angle, and you need to express that in terms of u, the sine of the same angle. Does nothing click?
     
  13. Feb 1, 2017 #12
    sorry limits are from 0 to 0.5 an oversight on my part..........
     
  14. Feb 1, 2017 #13
    i now get it lol
    ## 0.25∫{1-u^2}du ## from u=0 to u=0.5 thanks mate solution is ## 0.115##
     
  15. Feb 1, 2017 #14
    Why don't you try splitting ##cos^34x## into ##cos4x## and another term containing the term used for ##u## substitution?
     
  16. Feb 1, 2017 #15
    i have seen the obstacle with that move.........
     
  17. Feb 1, 2017 #16
    i have seen it, check post 13
     
  18. Feb 2, 2017 #17

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    @chwala
    Actually that is the move you finally made to solve. Check the time of @Eclair_de_XII 's post and your posts.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Integration problem using substitution
Loading...