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Simple cosine expression NOT so simple!

  1. Mar 29, 2007 #1

    I am rediscovering my long lost "A" level maths and have been having lots of fun working on puzzles. Unfortunately, I seem to have hit something of a wall in the following simple expression that is repelling every attack I launch:


    I have tried substituting x=arccos(w) and w=arccos(w/k), expressing things as logs, mungeing the equations I get, and a number of slightly more desperate attacks, but whatever I do to get rid of one term or provide something that can be cancelled out, a new problem pops up.

    I feel that there is a simple answer to this, but the more I look at it the less I can see the way forward.

    Any suggestions anyone?
    Last edited by a moderator: Mar 29, 2007
  2. jcsd
  3. Mar 29, 2007 #2


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    What exactly do you want to do with f(x)?
  4. Mar 29, 2007 #3
    Ah! So absorbed by it, I've missed the most important bit!

    I'm trying to integrate it to get the area under the curve between x=0 and x=pi
  5. Mar 29, 2007 #4
    Sorry, i couldn't get ur expression. is it (1+kcos(x))^(1/2)
  6. Mar 29, 2007 #5
    Yes it is - the root of (1+kcos(x))
  7. Mar 29, 2007 #6
    I don't think it has a solution made up entirely of elementary functions. Elliptic functions may be involved.
  8. Mar 29, 2007 #7
    I too struggled for it for 6-8 months. Its a kind of elliptic integral(which i didn't knew). u might be knowing. u can check it on an integrator at www.wolfram.com
  9. Mar 29, 2007 #8
    Gosh - what a great tip. I didn't know the integrator existed. Thank you.

    Having got the answer from Wolfram I'm kind of pleased that I hadn't missed an obvious solution.

    Thank you all.
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