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Integration Question

  1. Aug 1, 2010 #1
    What method of integration would I use to find the anti-derivative of

    [tex]\int sin(3u(t)) dt[/tex]

    when

    [tex]u(t)[/tex]

    Is and unknown function of time?
     
  2. jcsd
  3. Aug 1, 2010 #2
    It depends, because there are many elementary functions that U could be that would make this a nonelementary integral.
     
  4. Aug 1, 2010 #3
    I mean if

    [tex]u(t)[/tex]

    is completely unknown, is there no way to just generally integrate it even using terms like

    [tex]u'(t)[/tex]?


    [tex]\frac{-1}{3u'(t)}cos(3u(t))[/tex]
    seems to be sort of close if you differentiate it... But this is an incorrect usage of U substitution.
     
  5. Aug 1, 2010 #4
    If u(t) is unknown, you can not integrate numerically, and in general
    if u(t) is anything more complex than a linear function in t, the integral
    will involve error functions.

    For example, if u(t) = t, your antiderivative in post # 3 would be correct.
    Similarly if u(t) = kt +b with k and b constants
     
  6. Aug 1, 2010 #5
    What do you mean by error functions? Could you give me an example of such a situation? I am not exact familiar with that.
     
  7. Aug 2, 2010 #6
    Go to www.wolframAlpha.com

    Type in " integral e^ (3x^2) dx " [omit quotes] and hit return.
    See the erf error function in the answer ?

    Then clear and

    Type in erf x and hit return
    Put the cursor over the lower right "erf is the error function"
    and click on definition


    Note that if you change 3x^2 to 3x, the error function is not needed.
     
  8. Aug 2, 2010 #7
    Okay, thanks. I know what you mean now... I actually feel kinda stupid lol. I've actually found exact error from numerical solutions of different orders.
     
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