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Simple Integration by Substitution

  1. Aug 19, 2004 #1
    Please help. I'm having trouble with a simple integration by substitution problem


    The integrand is f(x) = x* sqr(x-1)
    The interval [1,2]

    Please draw it out in a gif file and send it to me via email.

    -much appreciated.
     
  2. jcsd
  3. Aug 19, 2004 #2

    Math Is Hard

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    If I tell you how to do the substitution will you try to work it out from there? Or do you want someone to just do your homework for you?
     
  4. Aug 19, 2004 #3

    Gokul43201

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    adiles,

    The policy here is that we'll help you if you show what you've tried and where you appear to be stuck.

    It seems to me that you may have a problem with algebra (in this case, at least), as the most obvious substitution should get you an easily integrable form.
     
  5. Aug 19, 2004 #4
    Start with [tex]u=\sqrt{x-1}[/tex]
     
  6. Aug 19, 2004 #5

    Math Is Hard

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    I wouldn't recommend that.
    (but I am interested to see how you worked it out with that sub!)
     
  7. Aug 19, 2004 #6
    and why not?
    ::
    u=sqrt(x-1)
    x=u^2+1
    dx=2udu

    The integrand becomes (u^2+1)u*2udu
    A simple polynomial which has to be integrated from 0 to 1 if i am not mistaken with calculations that are going in my head.
    ::

    -- AI
     
    Last edited: Aug 19, 2004
  8. Aug 19, 2004 #7

    Gokul43201

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    Tenali, I wish you hadn't done that in the thread. This leaves adiles with no work to do.
     
  9. Aug 19, 2004 #8

    Math Is Hard

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    I would use a slightly different (and simpler in my mind) substitution method, but I'll withhold, just to leave a little mystery and hopefully some "pleasure of discovery" for adiles. :smile:
     
  10. Aug 20, 2004 #9
    since some one already solved it for him, the simplest sub i saw was...

    f(x) = x* sqr(x-1)

    let
    u = x-1
     
    Last edited by a moderator: Aug 20, 2004
  11. Aug 20, 2004 #10

    Hurkyl

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    That's why you make the one example something different (but similar enough to demonstrate the point... maybe [itex]\int \sqrt{x-1} \, dx[/itex]) The problem is that all the example in the world usually don't help unless the student actually does a few himself.
     
  12. Aug 21, 2004 #11

    cronxeh

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    why the hell was my solution erased from this thread?
     
  13. Aug 22, 2004 #12
    Cronxeh im guessing

     
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