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Very Simple Question, please help: Integral of a derivative squared 
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#1
Jun508, 01:19 PM

P: 6

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
Jun508, 01:40 PM

P: 677

I think partial integration can work.



#3
Jun508, 01:43 PM

P: 70

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? 


#4
Jun508, 01:53 PM

P: 677

Very Simple Question, please help: Integral of a derivative squared
Wait a second is x(t) explicitly known?



#5
Jun508, 02:26 PM

P: 6

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! 


#6
Jun508, 02:59 PM

Math
Emeritus
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Thanks
PF Gold
P: 39,345

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 antiderivative. 


#7
Jun508, 02:59 PM

P: 677

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] 


#8
Jun508, 04:27 PM

P: 6

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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