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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]



    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


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


    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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