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integration question

Discussion in 'Mathematics' started by fudgesweets, Mar 2, 2011.

  1. fudgesweets

    fudgesweets New commenter

    How would you integrate 4*sqrt(1+3(cosx)^2)......any ideas for a substitution? perhaps?
     
  2. fudgesweets

    fudgesweets New commenter

    How would you integrate 4*sqrt(1+3(cosx)^2)......any ideas for a substitution? perhaps?
     
  3. DM

    DM New commenter

    Where does the question come from? I think it is an elliptical integral of the second kind.
     
  4. Colleen_Young

    Colleen_Young Occasional commenter

  5. Colleen_Young

    Colleen_Young Occasional commenter

  6. DM

    DM New commenter

    I used an invention that predates WA Casy ... my eyes.
     
  7. Karvol

    Karvol Occasional commenter

    Ouch.
     
  8. David Getling

    David Getling Senior commenter

    I'd also like to know where this came from, as I had a good play with this and didn't get anywhere. Like DM, my first thought was elliptical. If this really was in an A-level exam I'd imagine there were limits given, with the expectation of using a numerical method: in which case the OP should have said so.
     
  9. quick estimate 2*cos(2*x)+6 , integrates to sin(2*x) + 6*x.
    also try fourier series ,
    even function !, so limits -a,a integrates to zero.
    all b(n) coefficients zero apparently
    a0 + a1*cos(?) + a2*cos(?) +
    approximate function then integrate term by term perhaps.


     
  10. Colleen_Young

    Colleen_Young Occasional commenter

    DM - I do know you can integrate stuff (so can I), your wording amused me for some reason when I read it, reminded me of WolframAlpha which is one seriously useful resource.
    It even has Polecat's 19.4 (well, 19.3769 approx, more digits if you want)
    WolframAlpha


     
  11. I used Maple rather than Mathematica - personal preference.
    If I have the time, I might see what sort of accuracy Simpson's
    rule produces with not too many ordinates.

     

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