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

by gilgtc
Tags: derivative, integral, simple, squared
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Jun5-08, 01:19 PM
P: 6

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.


Thanks a lot!
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Jun5-08, 01:40 PM
P: 682
I think partial integration can work.
Nick R
Jun5-08, 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


Jun5-08, 01:53 PM
P: 682
Very Simple Question, please help: Integral of a derivative squared

Wait a second is x(t) explicitly known?
Jun5-08, 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?

Jun5-08, 02:59 PM
Sci Advisor
PF Gold
P: 39,556
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
even has an elementary anti-derivative.
Jun5-08, 02:59 PM
P: 682
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]
Jun5-08, 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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