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Very Simple Question, please help: Integral of a derivative squared

  1. Jun 5, 2008 #1
    Hello,

    I am trying to figure out how to integrate this, I know it must be simple but I am not sure how to do it.

    [tex]\int(\frac{dx}{dt})^{2}dt[/tex]


    Thanks a lot!
     
  2. jcsd
  3. Jun 5, 2008 #2
    I think partial integration can work.
     
  4. Jun 5, 2008 #3
    You just need x defined in terms of t

    x = x(t)

    then you can differentiate with respect to t,

    then you square dx/dt

    then you integrate that across t from t1 to t2

    right?
     
    Last edited: Jun 5, 2008
  5. Jun 5, 2008 #4
    Wait a second is x(t) explicitly known?
     
  6. Jun 5, 2008 #5
    hi, thanks for your answers. x(t) is not known that is why I am not sure how to do it. Otherwise what Nick mentioned would be easily applicable.

    Any other ideas? What do you mean by partial integration dirk_mec1?

    Thanks!
     
  7. Jun 5, 2008 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    He means "integration by parts". Do you have any reason to think that there is any simple answer to this question? I can see no reason to assume that
    [tex]\right(\frac{dx}{dt}\)^2[/tex]
    even has an elementary anti-derivative.
     
  8. Jun 5, 2008 #7
    I dont think you can just integrate [tex] \int (f'(x))^2 \mbox{d}x[/tex], right? The integration by parts(thanks hallsofIvy ) however gives:

    [tex] x (x'(t))^2 - \int x \cdot 2x' \cdot x''\ \mbox{d}t [/tex]
     
    Last edited: Jun 5, 2008
  9. Jun 5, 2008 #8
    re

    I thought that there was an easy equivalence like:

    [tex]\int(dx/dt)dt = x[/tex]

    I guess not! thanks for your help in any case.
     
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